Why distance is area under velocity-time line

WEBVTT
Kind: captions
Language: en

00:00:00.860 --> 00:00:02.240
Let's say I have
something moving

00:00:02.240 --> 00:00:07.990
with a constant velocity
of five meters per second.

00:00:07.990 --> 00:00:10.050
And we're just assuming
it's moving to the right,

00:00:10.050 --> 00:00:12.800
just to give us a direction,
because this is a vector

00:00:12.800 --> 00:00:15.970
quantity, so it's moving in
that direction right over there.

00:00:15.970 --> 00:00:19.140
And let me plot its
velocity against time.

00:00:19.140 --> 00:00:23.624
So this is my velocity.

00:00:23.624 --> 00:00:25.040
So I'm actually
going to only plot

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the magnitude of the
velocity, and you

00:00:26.720 --> 00:00:29.220
can specify that like this.

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So this is the magnitude
of the velocity.

00:00:33.520 --> 00:00:39.810
And then on this axis
I'm going to plot time.

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So we have a constant velocity
of five meters per second.

00:00:43.020 --> 00:00:45.720
So its magnitude is
five meters per second.

00:00:49.160 --> 00:00:50.240
And it's constant.

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It's not changing.

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As the seconds tick away the
velocity does not change.

00:00:54.470 --> 00:00:58.570
So it's just moving
five meters per second.

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Now, my question to you
is how far does this thing

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travel after five seconds?

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So after five seconds-- so
this is one second, two second,

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three seconds, four seconds,
five seconds, right over here.

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So how far did this thing
travel after five seconds?

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Well, we could think
about it two ways.

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One, we know that velocity
is equal to displacement over

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change in time.

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And displacement is
just change in position

00:01:32.770 --> 00:01:36.470
over change in time.

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Or another way to
think about it--

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If you multiply
both sides by change

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in time-- you get velocity
times change in time,

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is equal to displacement.

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So what was of the
displacement over here?

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Well, I know what
the velocity is--

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it's five meters per second.

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That's the velocity,
let me color-code this.

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That is the velocity.

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And we know what the change in
time is, it is five seconds.

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And so you get the seconds
cancel out the seconds,

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you get five times five-- 25
meters-- is equal to 25 meters.

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And that's pretty
straightforward.

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But the slightly more
interesting thing

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is that's exactly the area under
this rectangle right over here.

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What I'm going to show
you in this video,

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that is in general,
if you plot velocity,

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the magnitude of velocity.

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So you could say
speed to versus time.

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Or let me just stay
with the magnitude

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of the velocity versus time.

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The area under
that curve is going

00:02:38.300 --> 00:02:41.430
to be the distance traveled,
because, or the displacement.

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Because displacement is
just the velocity times

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the change in time.

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So if you just take out a
rectangle right over there.

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So let me draw a
slightly different one

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where the velocity is changing.

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So let me draw a situation
where you have a constant

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acceleration .

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The acceleration
over here is going

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to be one meter per
second, per second.

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So one meter per
second, squared.

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And let me draw the
same type of graph,

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although this is going to
look a little different now.

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So this is my velocity axis.

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I'll give myself a
little bit more space.

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So this is my velocity axis.

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I'm just going to draw the
magnitude of the velocity,

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and this right over
here is my time axis.

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So this is time.

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And let me mark
some stuff off here.

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So one, two, three, four, five,
six, seven, eight, nine, ten.

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And one, two, three, four, five,
six, seven, eight, nine, ten.

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And the magnitude
of velocity is going

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to be measured in
meters per second.

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And the time is going to
be measured in seconds.

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So my initial
velocity, or I could

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say the magnitude of
my initial velocity--

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so just my initial
speed, you could say,

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this is just a
fancy way of saying

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my initial speed is zero.

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So my initial speed is zero.

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So after one second
what's going to happen?

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After one second I'm going
one meter per second faster.

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So now I'm going one
meter per second.

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After two seconds,
whats happened?

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Well now I'm going another meter
per second faster than that.

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After another second--
if I go forward in time,

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if change in time is
one second, then I'm

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going a second faster than that.

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And if you remember the idea of
the slope from your algebra one

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class, that's exactly
what the acceleration

00:04:31.660 --> 00:04:34.260
is in this diagram
right over here.

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The acceleration, we
know that acceleration

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is equal to change in
velocity over change in time.

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Over here change in time
is along the x-axis.

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So this right over here
is a change in time.

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And this right over here
is a change in velocity.

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When we plot velocity or
the magnitude of velocity

00:04:59.550 --> 00:05:04.740
relative to time, the slope of
that line is the acceleration.

00:05:04.740 --> 00:05:08.070
And since we're assuming the
acceleration is constant,

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we have a constant slope.

00:05:09.560 --> 00:05:10.900
So we have just a line here.

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We don't have a curve.

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Now what I want to do is
think about a situation.

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Let's say that we accelerate it
one meter per second squared.

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And we do it for--
so the change in time

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is going to be five seconds.

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And my question to you is
how far have we traveled?

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Which is a slightly more
interesting question

00:05:32.760 --> 00:05:34.410
than what we've
been asking so far.

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So we start off with an
initial velocity of zero.

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And then for five
seconds we accelerate

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it one meter per second squared.

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So one, two, three, four, five.

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So this is where we go.

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This is where we are.

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So after five seconds,
we know our velocity.

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Our velocity is now
five meters per second.

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But how far have we traveled?

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So we could think about
it a little bit visually.

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We could say, look, we could try
to draw rectangles over here.

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Maybe right over here,
we have the velocity

00:06:04.520 --> 00:06:05.800
of one meter per second.

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So if I say one meter per
second times the second,

00:06:07.910 --> 00:06:11.040
that'll give me a
little bit of distance.

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And then the next one I have
a little bit more of distance,

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calculated the same way.

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I could keep drawing
these rectangles here,

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but then you're like, wait,
those rectangles are missing,

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because I wasn't for
the whole second,

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I wasn't only going
one meter per second.

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I kept accelerating.

00:06:23.870 --> 00:06:27.220
So I actually, I should maybe
split up the rectangles.

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I could split up the
rectangles even more.

00:06:30.180 --> 00:06:31.839
So maybe I go every half second.

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So on this half-second I
was going at this velocity.

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And I go that velocity
for a half-second.

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Velocity times the time would
give me the displacement.

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And I do it for the
next half second.

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Same exact idea here.

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Gives me the displacement.

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So on and so forth.

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But I think what you see as
you're getting-- is the more

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accurate-- the smaller
the rectangles,

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you try to make here, the closer
you're going to get to the area

00:06:55.530 --> 00:06:57.570
under this curve.

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And just like the
situation here.

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This area under
the curve is going

00:07:06.150 --> 00:07:07.325
to be the distance traveled.

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And lucky for us, this is
just going to be a triangle,

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and we know how to figure
out the area for triangle.

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So the area of a triangle
is equal to one half

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times base times height.

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Which hopefully
makes sense to you,

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because if you just
multiply base times height,

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you get the area for
the entire rectangle,

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and the triangle is
exactly half of that.

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So the distance traveled
in this situation,

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or I should say
the displacement,

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just because we want to make
sure we're focused on vectors.

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The displacement
here is going to be--

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or I should say the magnitude
of the displacement,

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maybe, which is the same
thing as the distance,

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is going to be one
half times the base,

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which is five seconds,
times the height,

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which is five meters per second.

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Times five meters.

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Let me do that in another color.

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Five meters per second.

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The seconds cancel
out with the seconds.

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And we're left with one half
times five times five meters.

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So it's one half times 25,
which is equal to 12.5 meters.

00:08:19.056 --> 00:08:21.180
And so there's an interesting
thing here, well one,

00:08:21.180 --> 00:08:22.805
there's a couple of
interesting things.

00:08:22.805 --> 00:08:25.280
Hopefully you'll realize that
if you're plotting velocity

00:08:25.280 --> 00:08:28.532
versus time, the
area under the curve,

00:08:28.532 --> 00:08:30.240
given a certain amount
of time, tells you

00:08:30.240 --> 00:08:32.049
how far you have traveled.

00:08:32.049 --> 00:08:34.840
The other interesting thing
is that the slope of the curve

00:08:34.840 --> 00:08:36.559
tells you your acceleration.

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What's the slope over here?

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Well, It's completely flat.

00:08:39.182 --> 00:08:41.140
And that's because the
velocity isn't changing.

00:08:41.140 --> 00:08:45.500
So in this situation, we
have a constant acceleration.

00:08:45.500 --> 00:08:48.550
The magnitude of that
acceleration is exactly zero.

00:08:48.550 --> 00:08:50.460
Our velocity is not changing.

00:08:50.460 --> 00:08:53.790
Here we have an acceleration of
one meter per second squared,

00:08:53.790 --> 00:08:57.370
and that's why the slope of this
line right over here is one.

00:08:57.370 --> 00:08:59.474
The other interesting
thing, is, if even

00:08:59.474 --> 00:09:00.890
if you have constant
acceleration,

00:09:00.890 --> 00:09:02.515
you could still figure
out the distance

00:09:02.515 --> 00:09:04.972
by just taking the area
under the curve like this.

00:09:04.972 --> 00:09:06.430
We were able to
figure out there we

00:09:06.430 --> 00:09:09.220
were able to get 12.5 meters.

00:09:09.220 --> 00:09:11.582
The last thing I want to
introduce you to-- actually,

00:09:11.582 --> 00:09:13.040
let me just do it
until next video,

00:09:13.040 --> 00:09:15.750
and I'll introduce you to
the idea of average velocity.

00:09:15.750 --> 00:09:17.810
Now that we feel
comfortable with the idea,

00:09:17.810 --> 00:09:19.940
that the distance
you traveled is

00:09:19.940 --> 00:09:24.672
the area under the
velocity versus time curve.


Airbus A380 take-off time

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:05.440
This right here is a picture
of an Airbus A380 aircraft.

00:00:05.440 --> 00:00:08.109
And I was curious
how long would it

00:00:08.109 --> 00:00:10.790
take this aircraft to take off?

00:00:10.790 --> 00:00:12.875
And I looked up its
takeoff velocity.

00:00:17.570 --> 00:00:23.600
And the specs I got were
280 kilometers per hour.

00:00:23.600 --> 00:00:26.810
And to make this a velocity we
have to specify a direction as

00:00:26.810 --> 00:00:28.620
well, not just a magnitude.

00:00:28.620 --> 00:00:31.680
So the direction is in the
direction of the runway.

00:00:31.680 --> 00:00:35.304
So that would be the positive
direction right over there.

00:00:35.304 --> 00:00:37.470
So when we're talking about
acceleration or velocity

00:00:37.470 --> 00:00:38.928
in this, we're
going to assume it's

00:00:38.928 --> 00:00:42.780
in this direction, the direction
of going down the runway.

00:00:42.780 --> 00:00:44.970
And I also looked up
its specs, and this,

00:00:44.970 --> 00:00:47.120
I'm simplifying a little
bit, because it's not

00:00:47.120 --> 00:00:49.214
going to have a purely
constant acceleration.

00:00:49.214 --> 00:00:50.630
But let's just say
from the moment

00:00:50.630 --> 00:00:53.490
that the pilot says we're
taking off to when it actually

00:00:53.490 --> 00:00:55.690
takes off it has a
constant acceleration.

00:00:55.690 --> 00:01:02.280
Its engines are able to
provide a constant acceleration

00:01:02.280 --> 00:01:09.960
of 1.0 meters per
second per second.

00:01:09.960 --> 00:01:13.070
So after every second it
can go one meter per second

00:01:13.070 --> 00:01:16.030
faster than it was going at
the beginning of that second.

00:01:16.030 --> 00:01:25.530
Or another way to write this
is 1.0-- let me write it

00:01:25.530 --> 00:01:27.250
this way-- meters
per second per second

00:01:27.250 --> 00:01:30.984
can also be written as
meters per second squared.

00:01:30.984 --> 00:01:32.650
I find this a little
bit more intuitive.

00:01:32.650 --> 00:01:34.910
This is a little
bit neater to write.

00:01:34.910 --> 00:01:36.360
So let's figure this out.

00:01:36.360 --> 00:01:38.490
So the first thing
we're trying to answer

00:01:38.490 --> 00:01:42.540
is, how long does take off last?

00:01:47.360 --> 00:01:50.200
That is the question
we will try to answer.

00:01:50.200 --> 00:01:52.400
And to answer this,
at least my brain

00:01:52.400 --> 00:01:54.289
wants to at least
get the units right.

00:01:54.289 --> 00:01:55.830
So over here we have
our acceleration

00:01:55.830 --> 00:01:58.890
in terms of meters and
seconds, or seconds squared.

00:01:58.890 --> 00:02:00.640
And over here we have
our takeoff velocity

00:02:00.640 --> 00:02:04.130
in terms of
kilometers and hours.

00:02:04.130 --> 00:02:06.030
So let's just convert
this takeoff velocity

00:02:06.030 --> 00:02:07.170
into meters per second.

00:02:07.170 --> 00:02:10.479
And then it might simplify
answering this question.

00:02:10.479 --> 00:02:14.770
So if we have 280
kilometers per hour,

00:02:14.770 --> 00:02:18.170
how do we convert that
to meters per second?

00:02:18.170 --> 00:02:21.630
So let's convert it to
kilometers per second first.

00:02:21.630 --> 00:02:23.650
So we want to get
rid of this hours.

00:02:23.650 --> 00:02:25.122
And the best way
to do that, if we

00:02:25.122 --> 00:02:26.580
have an hour in
the denominator, we

00:02:26.580 --> 00:02:29.230
want an hour in the
numerator, and we

00:02:29.230 --> 00:02:31.530
want a second in
the denominator.

00:02:31.530 --> 00:02:34.600
And so what do we
multiply this by?

00:02:34.600 --> 00:02:36.960
Or what do we put in front
of the hours and seconds?

00:02:36.960 --> 00:02:41.030
So one hour, in one hour
there are 3,600 seconds,

00:02:41.030 --> 00:02:44.960
60 seconds in a minute,
60 minutes in an hour.

00:02:44.960 --> 00:02:46.870
And so you have one
of the larger unit

00:02:46.870 --> 00:02:50.400
is equal to 3,600
of the smaller unit.

00:02:50.400 --> 00:02:52.280
And that we can
multiply by that.

00:02:52.280 --> 00:02:54.820
And if we do that, the
hours will cancel out.

00:02:54.820 --> 00:02:58.950
And we'll get 280 divided by
3,600 kilometers per second.

00:02:58.950 --> 00:03:00.830
But I want to do
all my math at once.

00:03:00.830 --> 00:03:04.550
So let's also do the conversion
from kilometers to meters.

00:03:04.550 --> 00:03:08.770
So once again, we have
kilometers in the numerator.

00:03:08.770 --> 00:03:11.070
So we want the kilometers
in the denominator now.

00:03:11.070 --> 00:03:12.410
So it cancels out.

00:03:12.410 --> 00:03:14.490
And we want meters
in the numerator.

00:03:14.490 --> 00:03:15.710
And what's the smaller unit?

00:03:15.710 --> 00:03:16.790
It's meters.

00:03:16.790 --> 00:03:20.800
And we have 1,000 meters
for every 1 kilometer.

00:03:20.800 --> 00:03:22.830
And so when you multiply
this out the kilometers

00:03:22.830 --> 00:03:23.910
are going to cancel out.

00:03:23.910 --> 00:03:29.490
And you are going to be
left with 280 times 1,

00:03:29.490 --> 00:03:35.620
so we don't have to write
it down, times 1,000,

00:03:35.620 --> 00:03:43.400
all of that over 3,600,
and the units we have left

00:03:43.400 --> 00:03:49.440
are meters per-- and the
only unit we have left here

00:03:49.440 --> 00:03:52.700
is second-- meters per second.

00:03:52.700 --> 00:03:57.970
So let's get my trusty TI-85
out and actually calculate this.

00:03:57.970 --> 00:04:03.050
So we have 280 times 1000, which
is obviously 280,000, but let

00:04:03.050 --> 00:04:06.790
me just divide that by 3,600.

00:04:06.790 --> 00:04:10.880
And it gives me 77.7
repeating indefinitely.

00:04:10.880 --> 00:04:13.300
And it looks like I had
two significant digits

00:04:13.300 --> 00:04:15.120
in each of these
original things.

00:04:15.120 --> 00:04:18.230
I had 1.0 over
here, not 100% clear

00:04:18.230 --> 00:04:20.630
how many significant
digits over here.

00:04:20.630 --> 00:04:23.830
Was the spec rounded to
the nearest 10 kilometers?

00:04:23.830 --> 00:04:26.799
Or is it exactly 280
kilometers per hour?

00:04:26.799 --> 00:04:28.340
Just to be safe I'll
assume that it's

00:04:28.340 --> 00:04:30.360
rounded to the
nearest 10 kilometers.

00:04:30.360 --> 00:04:32.390
So we only have two
significant digits here.

00:04:32.390 --> 00:04:34.265
So we should only have
two significant digits

00:04:34.265 --> 00:04:34.910
in our answer.

00:04:34.910 --> 00:04:41.390
So we're going to round this
to 78 meters per second.

00:04:41.390 --> 00:04:48.800
So this is going to be
78 meters per second,

00:04:48.800 --> 00:04:50.950
which is pretty fast.

00:04:50.950 --> 00:04:53.590
For this thing to take off
every second that goes by it

00:04:53.590 --> 00:04:58.260
has to travel 78
meters, roughly 3/4

00:04:58.260 --> 00:05:01.369
of the length of a football
field in every second.

00:05:01.369 --> 00:05:03.160
But that's not what
we're trying to answer.

00:05:03.160 --> 00:05:05.950
We're trying to say how
long will take off last?

00:05:05.950 --> 00:05:09.650
Well we could just do this in
our head if you think about it.

00:05:09.650 --> 00:05:12.440
The acceleration is 1 meter
per second, per second.

00:05:12.440 --> 00:05:15.060
Which tells us
after every second

00:05:15.060 --> 00:05:17.420
it's going 1 meter
per second faster.

00:05:17.420 --> 00:05:21.574
So if you start at a velocity
of 0 and then after 1 second

00:05:21.574 --> 00:05:22.990
it'll be going 1
meter per second.

00:05:22.990 --> 00:05:25.198
After 2 seconds it will be
going 2 meters per second.

00:05:25.198 --> 00:05:27.740
After 3 seconds it'll be
going 3 meters per second.

00:05:27.740 --> 00:05:30.770
So how long will it take to
get to 78 meters per second?

00:05:30.770 --> 00:05:38.550
Well, it will take 78
seconds, or roughly a minute

00:05:38.550 --> 00:05:40.710
and 18 seconds.

00:05:40.710 --> 00:05:44.840
And just to verify this with our
definition of our acceleration,

00:05:44.840 --> 00:05:46.877
so to speak, just
remember acceleration,

00:05:46.877 --> 00:05:48.960
which is a vector quantity,
and all the directions

00:05:48.960 --> 00:05:51.060
we're talking about now
are in the direction

00:05:51.060 --> 00:05:53.280
of this direction of the runway.

00:05:53.280 --> 00:06:00.240
The acceleration is equal
to change in velocity

00:06:00.240 --> 00:06:02.140
over change in time.

00:06:04.676 --> 00:06:07.050
And we're trying to solve for
how much time does it take,

00:06:07.050 --> 00:06:08.740
or the change in time.

00:06:08.740 --> 00:06:09.520
So let's do that.

00:06:09.520 --> 00:06:12.040
So let's multiply both
sides by change in time.

00:06:12.040 --> 00:06:17.780
You get change in time
times acceleration

00:06:17.780 --> 00:06:20.785
is equal to change in velocity.

00:06:24.180 --> 00:06:26.600
And to solve for change
in time, divide both sides

00:06:26.600 --> 00:06:29.230
by the acceleration.

00:06:29.230 --> 00:06:31.940
So divide both sides by
the acceleration you get

00:06:31.940 --> 00:06:33.980
a change in time.

00:06:33.980 --> 00:06:35.710
I could go down
here, but I just want

00:06:35.710 --> 00:06:37.584
to use all this real
estate I have over here.

00:06:37.584 --> 00:06:40.400
I have change in time
is equal to change

00:06:40.400 --> 00:06:44.855
in velocity divided
by acceleration.

00:06:47.920 --> 00:06:51.664
And in this situation, what
is our change in velocity?

00:06:51.664 --> 00:06:53.455
Well, we're starting
off with the velocity,

00:06:53.455 --> 00:06:54.980
or we're assuming
we're starting off

00:06:54.980 --> 00:06:57.880
with a velocity of
0 meters per second.

00:06:57.880 --> 00:07:00.710
And we're getting up to
78 meters per second.

00:07:00.710 --> 00:07:04.650
So our change in velocity
is the 78 meters per second.

00:07:09.230 --> 00:07:11.030
So this is equal,
in our situation,

00:07:11.030 --> 00:07:14.580
78 meters per second is
our change in velocity.

00:07:14.580 --> 00:07:17.400
I'm taking the final velocity,
78 meters per second,

00:07:17.400 --> 00:07:19.320
and subtract from that
the initial velocity,

00:07:19.320 --> 00:07:20.590
which is 0 meters per second.

00:07:20.590 --> 00:07:22.000
And you just get this.

00:07:22.000 --> 00:07:24.230
Divided by the
acceleration, divided

00:07:24.230 --> 00:07:28.990
by 1 meter per
second per second,

00:07:28.990 --> 00:07:31.400
or 1 meter per second squared.

00:07:31.400 --> 00:07:33.160
So the numbers part
are pretty easy.

00:07:33.160 --> 00:07:36.920
You have 78 divided by
1, which is just 78.

00:07:36.920 --> 00:07:40.140
And then the units you
have meters per second.

00:07:40.140 --> 00:07:42.620
And then if you divide by
meters per second squared,

00:07:42.620 --> 00:07:44.230
that's the same
thing as multiplying

00:07:44.230 --> 00:07:46.760
by seconds squared per meter.

00:07:46.760 --> 00:07:48.440
Right?

00:07:48.440 --> 00:07:49.940
Dividing by something
the same thing

00:07:49.940 --> 00:07:51.940
as multiplying by
its reciprocal.

00:07:51.940 --> 00:07:54.130
And you can do the
same thing with units.

00:07:54.130 --> 00:07:57.110
And then we see the
meters cancel out.

00:07:57.110 --> 00:07:59.060
And then seconds squared
divided by seconds,

00:07:59.060 --> 00:08:00.660
you're just left with seconds.

00:08:00.660 --> 00:08:04.340
So once again, we
get 78 seconds,

00:08:04.340 --> 00:08:07.910
a little over a minute for
this thing to take off.


Race cars with constant speed around curve

WEBVTT
Kind: captions
Language: en

00:00:00.760 --> 00:00:04.400
So we have some race
cars racing, right here.

00:00:04.400 --> 00:00:07.480
And I have an interesting
question to ask you.

00:00:07.480 --> 00:00:11.450
If we assume that these
cars are making this turn

00:00:11.450 --> 00:00:12.930
right over here,
that all of them

00:00:12.930 --> 00:00:21.720
are making this turn at
a constant speed of 100

00:00:21.720 --> 00:00:28.980
kilometers per hour, my
interesting question for you

00:00:28.980 --> 00:00:34.510
is, are these cars accelerating
while they make this turn?

00:00:34.510 --> 00:00:36.335
So is acceleration happening?

00:00:39.270 --> 00:00:43.110
And you might say, well, gee,
look, my speed was constant,

00:00:43.110 --> 00:00:44.090
it's not changing.

00:00:44.090 --> 00:00:46.052
If I looked at the
speedometer for the car

00:00:46.052 --> 00:00:48.010
here, if I looked at the
speedometer over here,

00:00:48.010 --> 00:00:51.720
it won't budge, it just stays
at 100 kilometers per hour.

00:00:51.720 --> 00:00:54.790
I don't have any change
in speed over time.

00:00:54.790 --> 00:00:56.530
And so then you
might say that you

00:00:56.530 --> 00:00:58.552
don't have any acceleration.

00:00:58.552 --> 00:01:00.010
But then you might
be saying, well,

00:01:00.010 --> 00:01:01.940
why would Sal even
make this video?

00:01:01.940 --> 00:01:04.360
And why would that question
even be interesting?

00:01:04.360 --> 00:01:07.860
And your second
suspicion would be true,

00:01:07.860 --> 00:01:13.520
because these cars
actually are accelerating

00:01:13.520 --> 00:01:15.960
despite having a constant speed.

00:01:15.960 --> 00:01:18.630
And you can pause it and
think about that for a second,

00:01:18.630 --> 00:01:19.317
if want to.

00:01:19.317 --> 00:01:20.900
But I wanted to point
this out to you,

00:01:20.900 --> 00:01:24.840
because in an example like this,
the difference between speed

00:01:24.840 --> 00:01:27.570
and velocity starts
to matter, speed

00:01:27.570 --> 00:01:30.800
being a scalar quantity
only having a magnitude.

00:01:30.800 --> 00:01:33.120
And velocity being
a vector quantity,

00:01:33.120 --> 00:01:35.640
being speed with a
direction, having

00:01:35.640 --> 00:01:37.680
a magnitude and a direction.

00:01:37.680 --> 00:01:41.250
And to think about-- let's
take a top view of this thing,

00:01:41.250 --> 00:01:43.720
and then I think it'll
become a little bit clearer

00:01:43.720 --> 00:01:45.782
the difference between
speed and velocity

00:01:45.782 --> 00:01:47.365
and why these things
are accelerating.

00:01:47.365 --> 00:01:50.160
So if I were to take a top
view of this racetrack--

00:01:50.160 --> 00:01:52.450
I'll do my best
attempt to draw it--

00:01:52.450 --> 00:01:55.350
so it might look
something like this.

00:01:55.350 --> 00:01:56.950
This is the top view.

00:01:56.950 --> 00:01:59.530
I could even draw
this red and white.

00:01:59.530 --> 00:02:03.650
So red, just to
give you the idea.

00:02:03.650 --> 00:02:08.230
So this is the red, and
there's some white in between.

00:02:08.230 --> 00:02:09.979
Obviously I'm not
drawing as many dividers

00:02:09.979 --> 00:02:11.437
as there are in
the actual picture,

00:02:11.437 --> 00:02:13.970
but it gives you an idea of
what I'm actually drawing.

00:02:13.970 --> 00:02:15.910
And then there's
some grass out here,

00:02:15.910 --> 00:02:18.150
there's some grass
over here, and then

00:02:18.150 --> 00:02:21.050
there's some grass over here.

00:02:21.050 --> 00:02:23.580
And let's focus on this orange
car and this red car right

00:02:23.580 --> 00:02:26.240
over here.

00:02:26.240 --> 00:02:29.500
And this is a top view, so this
is its path right over here.

00:02:29.500 --> 00:02:31.300
And we're saying it
has a constant speed

00:02:31.300 --> 00:02:33.630
of 100 kilometers per hour.

00:02:33.630 --> 00:02:36.640
So if you think
about its velocity,

00:02:36.640 --> 00:02:39.610
the magnitude of it's
velocity is constant,

00:02:39.610 --> 00:02:41.750
it's 100 kilometers per hour.

00:02:41.750 --> 00:02:44.670
But what is happening to the
direction of the velocity?

00:02:44.670 --> 00:02:47.030
Remember, velocity
is a vector quantity.

00:02:47.030 --> 00:02:49.450
It has magnitude and direction.

00:02:49.450 --> 00:02:52.570
So up here, when it's
starting to enter the curve,

00:02:52.570 --> 00:02:54.990
it's going in this direction.

00:02:54.990 --> 00:02:58.039
And you tend to show
vectors by arrows like this.

00:02:58.039 --> 00:02:59.580
And what you do is,
the arrow's going

00:02:59.580 --> 00:03:02.660
in the direction of the
velocity, in this case,

00:03:02.660 --> 00:03:05.910
and normally you would draw
the length of the arrow shows

00:03:05.910 --> 00:03:06.950
what is the velocity.

00:03:06.950 --> 00:03:09.290
The magnitude of the
velocity, I should say.

00:03:09.290 --> 00:03:10.580
So it's velocity's constant.

00:03:10.580 --> 00:03:13.090
So the length of this arrow
will always be constant.

00:03:13.090 --> 00:03:14.950
But as we see, it's
direction changes.

00:03:14.950 --> 00:03:16.457
When it's halfway
through the turn,

00:03:16.457 --> 00:03:18.040
it's not going in
that same direction.

00:03:18.040 --> 00:03:19.950
It is now going in a
different direction,

00:03:19.950 --> 00:03:21.783
and when it comes to
the bottom of the turn,

00:03:21.783 --> 00:03:23.600
it's going in a very
different direction.

00:03:23.600 --> 00:03:27.109
And the direction keeps changing
as long as it is turning.

00:03:27.109 --> 00:03:28.900
And I'm not going to
go into the math here.

00:03:28.900 --> 00:03:31.420
We're going to wait for the
math on this a little bit later.

00:03:31.420 --> 00:03:37.210
But remember, acceleration is
a change in velocity over time.

00:03:37.210 --> 00:03:46.760
Acceleration is equal to a
change in velocity over time,

00:03:46.760 --> 00:03:51.510
or we could say over
a change in time.

00:03:51.510 --> 00:03:55.360
And although the velocity's
magnitude is constant here,

00:03:55.360 --> 00:03:57.305
it's direction is changing.

00:04:00.670 --> 00:04:02.510
If there was no
acceleration on it,

00:04:02.510 --> 00:04:04.990
it's magnitude and the
direction of it's velocity

00:04:04.990 --> 00:04:07.300
would be constant,
and the car would just

00:04:07.300 --> 00:04:10.600
keep going in that direction.

00:04:10.600 --> 00:04:13.810
So somehow, the
car's direction is

00:04:13.810 --> 00:04:17.855
changing inward over
and over and over again.

00:04:17.855 --> 00:04:19.980
And so this is just kind
of a little bit of a trick

00:04:19.980 --> 00:04:22.000
question, something
for you to think about,

00:04:22.000 --> 00:04:24.660
we're going to discuss
the math in more

00:04:24.660 --> 00:04:26.510
detail in future videos.

00:04:26.510 --> 00:04:30.640
But what's happening here is the
cars actually are accelerating.

00:04:30.640 --> 00:04:32.990
And they're actually
accelerating inwards,

00:04:32.990 --> 00:04:34.800
and that's what's
changing inwards.

00:04:34.800 --> 00:04:37.440
And when I say inwards,
they're being accelerated

00:04:37.440 --> 00:04:42.890
towards the center of
the curve, and that's

00:04:42.890 --> 00:04:47.937
what's allowing their
direction to actually change.


Acceleration

WEBVTT
Kind: captions
Language: en

00:00:00.377 --> 00:00:02.960
In this video, I want to talk a
little bit about acceleration.

00:00:06.090 --> 00:00:08.130
And this is probably
an idea that you're

00:00:08.130 --> 00:00:09.600
somewhat familiar
with, or at least

00:00:09.600 --> 00:00:12.360
you've heard the term
used here or there.

00:00:12.360 --> 00:00:17.015
Acceleration is just the
change in velocity over time.

00:00:25.370 --> 00:00:28.280
Probably one of the most typical
examples of acceleration,

00:00:28.280 --> 00:00:30.420
if you're at all
interested in cars,

00:00:30.420 --> 00:00:33.000
is that many times
they will give you

00:00:33.000 --> 00:00:35.510
acceleration numbers, especially
for sport cars, actually

00:00:35.510 --> 00:00:38.350
all cars if you look
up in Consumer Reports,

00:00:38.350 --> 00:00:40.600
or wherever they give the
stats on different cars.

00:00:40.600 --> 00:00:44.840
They'll tell you something like,
I don't know, like a Porsche--

00:00:44.840 --> 00:00:48.410
and I'm going to make up
these numbers right over here.

00:00:48.410 --> 00:00:53.020
So let's say that we
have a Porsche 911.

00:00:53.020 --> 00:00:55.960
They'll say that a Porsche 911,
they'll literally measure it

00:00:55.960 --> 00:00:58.672
with a stopwatch, can go
0 to 60 miles per hour.

00:01:01.432 --> 00:01:02.890
And these aren't
the exact numbers,

00:01:02.890 --> 00:01:04.819
although I think it's
probably pretty close.

00:01:04.819 --> 00:01:08.130
0 to 60 miles per hour
in, let's say, 3 seconds.

00:01:13.194 --> 00:01:15.610
So, although officially what
they're giving you right here

00:01:15.610 --> 00:01:17.150
are speeds, because
they're only giving you

00:01:17.150 --> 00:01:18.730
magnitude and no
direction, you can

00:01:18.730 --> 00:01:20.355
assume that it's in
the same direction.

00:01:20.355 --> 00:01:22.680
I mean, We could
say, 0 miles per hour

00:01:22.680 --> 00:01:27.320
to the east to 60 miles per
hour to the east in 3 seconds.

00:01:27.320 --> 00:01:29.740
So what was the
acceleration here?

00:01:29.740 --> 00:01:32.480
So I just told you the
definition of acceleration.

00:01:32.480 --> 00:01:34.930
It's change in
velocity over time.

00:01:34.930 --> 00:01:37.660
So the acceleration-- and
once again acceleration

00:01:37.660 --> 00:01:39.420
is a vector quantity.

00:01:39.420 --> 00:01:41.990
You want to know not only
how much is velocity changing

00:01:41.990 --> 00:01:44.870
over time, you also care
about the direction.

00:01:44.870 --> 00:01:46.370
It also makes sense
because velocity

00:01:46.370 --> 00:01:48.580
itself is a vector quantity.

00:01:48.580 --> 00:01:51.060
It needs magnitude
and direction.

00:01:51.060 --> 00:01:53.210
So the acceleration
here-- and we're

00:01:53.210 --> 00:01:55.210
just going to assume
that we're going

00:01:55.210 --> 00:01:58.720
to the right, 0 miles per
hour and 60 miles per hour

00:01:58.720 --> 00:02:02.834
to the right-- so it's going
to be change in velocity.

00:02:02.834 --> 00:02:05.000
So let me just write it
down with different notation

00:02:05.000 --> 00:02:06.583
just so you could
familiarize yourself

00:02:06.583 --> 00:02:08.479
if you see it in the
textbook this way.

00:02:08.479 --> 00:02:12.780
So change in velocity.

00:02:12.780 --> 00:02:17.930
This delta symbol right
here just means "change in."

00:02:17.930 --> 00:02:21.580
Change in velocity over time.

00:02:21.580 --> 00:02:23.910
It's really, as I've
mentioned in previous videos,

00:02:23.910 --> 00:02:26.980
it's really time is
really a change in time.

00:02:26.980 --> 00:02:29.830
But we could just
write time here.

00:02:29.830 --> 00:02:31.710
This 3 seconds is
really change in time.

00:02:31.710 --> 00:02:35.282
It might have been, if you
looked at your second hand,

00:02:35.282 --> 00:02:37.740
it might have been 5 seconds
when it started, and then my 8

00:02:37.740 --> 00:02:40.850
seconds when it stopped, so
it took a total of 3 seconds.

00:02:40.850 --> 00:02:43.910
So time is really a
change in seconds.

00:02:43.910 --> 00:02:47.750
But we'll just go with time
right here, or just with a t.

00:02:47.750 --> 00:02:49.830
So what's our
change in velocity?

00:02:49.830 --> 00:02:52.780
So our final velocity
is 60 miles per hour.

00:02:55.700 --> 00:02:58.700
And our original velocity
was 0 miles per hour.

00:02:58.700 --> 00:03:03.950
So it's 60 minus
0 miles per hour.

00:03:03.950 --> 00:03:06.400
And then, what is our time?

00:03:06.400 --> 00:03:08.500
What is our time over here?

00:03:08.500 --> 00:03:12.240
Well, our time is, or we could
even say our change in time,

00:03:12.240 --> 00:03:14.260
our change in time is 3 seconds.

00:03:18.120 --> 00:03:22.890
So this gives us 20 miles
per hour, per second.

00:03:22.890 --> 00:03:24.310
Let me write this down.

00:03:24.310 --> 00:03:26.720
So this becomes,
this top part is 60.

00:03:26.720 --> 00:03:29.220
60 divided by 3 is 20.

00:03:29.220 --> 00:03:30.460
So we get 20.

00:03:30.460 --> 00:03:32.210
But then the units are
little bit strange.

00:03:32.210 --> 00:03:33.410
We have miles.

00:03:33.410 --> 00:03:40.800
Instead of writing MPH, I'm
going to write miles per hour.

00:03:40.800 --> 00:03:43.020
That's the same thing as MPH.

00:03:43.020 --> 00:03:45.800
And then we also, in the
denominator, right over here,

00:03:45.800 --> 00:03:52.040
have seconds.

00:03:52.040 --> 00:03:53.360
Which is a little bit strange.

00:03:53.360 --> 00:03:56.030
And as you'll see, the
units for acceleration

00:03:56.030 --> 00:03:57.390
do seem a little bit strange.

00:03:57.390 --> 00:03:58.490
But if we think it
through, it actually

00:03:58.490 --> 00:04:00.070
might make a little
bit of sense.

00:04:00.070 --> 00:04:01.632
So miles per hour.

00:04:01.632 --> 00:04:03.590
And then we could either
put seconds like this,

00:04:03.590 --> 00:04:06.332
or we could write per second.

00:04:06.332 --> 00:04:08.290
And let's just think
about what this is saying,

00:04:08.290 --> 00:04:10.040
and then we could get
it all into seconds,

00:04:10.040 --> 00:04:12.120
or we could all get into
hours, whatever we like.

00:04:12.120 --> 00:04:15.810
This is saying that every
second, this Porsche 911

00:04:15.810 --> 00:04:19.560
can increase its velocity
by 20 miles per hour.

00:04:19.560 --> 00:04:22.124
So its acceleration is 20
miles per hour, per second.

00:04:22.124 --> 00:04:24.040
And actually, we should
include the direction,

00:04:24.040 --> 00:04:26.200
because we're talking
about vector quantities.

00:04:26.200 --> 00:04:27.830
So this is to the east.

00:04:27.830 --> 00:04:32.220
So this is east, and then
this is east right over here--

00:04:32.220 --> 00:04:35.670
just so we make sure that
we're dealing with vectors.

00:04:35.670 --> 00:04:37.700
You're giving it a
direction, due east.

00:04:37.700 --> 00:04:40.350
So every second it can
increase in velocity

00:04:40.350 --> 00:04:41.690
by 20 miles per hour.

00:04:41.690 --> 00:04:42.605
So hopefully, with
the way I'm saying it,

00:04:42.605 --> 00:04:43.920
it makes a little bit of sense.

00:04:43.920 --> 00:04:46.390
20 miles per hour, per second.

00:04:46.390 --> 00:04:48.330
That's exactly what
this is talking about.

00:04:48.330 --> 00:04:50.240
Now we could also
write it like this.

00:04:50.240 --> 00:04:57.600
This is the same thing
as 20 miles per hour,

00:04:57.600 --> 00:04:59.670
because if you take
something and you

00:04:59.670 --> 00:05:02.640
divide by seconds, that's the
same thing as multiplying it

00:05:02.640 --> 00:05:04.070
by 1 over seconds.

00:05:04.070 --> 00:05:05.480
So that's miles
per hour-seconds.

00:05:08.220 --> 00:05:10.320
And although this
is correct, to me

00:05:10.320 --> 00:05:12.410
this makes a little
less intuitive sense.

00:05:12.410 --> 00:05:13.750
This one literally says it.

00:05:13.750 --> 00:05:17.010
Every second, it's increasing in
velocity by 20 miles per hour.

00:05:17.010 --> 00:05:20.424
20 miles per hour increase
in velocity per second.

00:05:20.424 --> 00:05:21.840
So that kind of
makes sense to me.

00:05:21.840 --> 00:05:25.150
Here it's saying 20
miles per hour-seconds.

00:05:25.150 --> 00:05:28.220
So once again, it's
not as intuitive.

00:05:28.220 --> 00:05:30.790
But we can make this so it's
all in one unit of time,

00:05:30.790 --> 00:05:33.260
although you don't
really have to.

00:05:33.260 --> 00:05:35.240
You can change this
so that you get rid

00:05:35.240 --> 00:05:37.080
of maybe the hours
in the denominator.

00:05:37.080 --> 00:05:39.496
And the best way to get rid
of an hour in the denominator,

00:05:39.496 --> 00:05:41.080
is by multiplying
it by something

00:05:41.080 --> 00:05:43.110
that has hours in the numerator.

00:05:43.110 --> 00:05:47.200
So hour and seconds.

00:05:47.200 --> 00:05:50.990
And here, the smaller
unit is the seconds.

00:05:50.990 --> 00:05:54.380
So it's 3,600 seconds
for every 1 hour.

00:05:54.380 --> 00:05:56.770
Or 1 hour is equal
to 3,600 seconds.

00:05:56.770 --> 00:06:01.060
Or 1/3600 of an hour per second.

00:06:01.060 --> 00:06:03.060
All of those are legitimate
ways to interpret

00:06:03.060 --> 00:06:06.050
this thing in magenta
right over here.

00:06:06.050 --> 00:06:09.030
And then you multiply, do a
little dimensional analysis.

00:06:09.030 --> 00:06:11.400
Hour cancels with hour.

00:06:11.400 --> 00:06:19.330
And then will be
equal to 20/3600.

00:06:19.330 --> 00:06:23.840
20/3600 miles per
seconds times seconds.

00:06:23.840 --> 00:06:27.560
Or we could say,
miles-- let me write

00:06:27.560 --> 00:06:31.500
it this way-- miles per
seconds times seconds.

00:06:31.500 --> 00:06:34.690
Or we could say,
miles per second-- I

00:06:34.690 --> 00:06:37.280
want to do that in
another color-- miles

00:06:37.280 --> 00:06:38.375
per second squared.

00:06:44.440 --> 00:06:46.030
And we can simplify
this a little bit.

00:06:46.030 --> 00:06:48.700
Divide the numerator
and denominator by 10.

00:06:48.700 --> 00:06:51.450
You get 2/360.

00:06:51.450 --> 00:06:53.300
Or you could get,
this is the same thing

00:06:53.300 --> 00:07:04.210
as, 1/180 miles
per second squared.

00:07:04.210 --> 00:07:05.980
And I'll just
abbreviate it like that.

00:07:05.980 --> 00:07:10.040
And once again, this 1/180
of a mile, how much is that?

00:07:10.040 --> 00:07:11.457
You might want to
convert to feet.

00:07:11.457 --> 00:07:13.040
But the whole point
in here is, I just

00:07:13.040 --> 00:07:14.830
wanted to show you
that, well, one, how

00:07:14.830 --> 00:07:16.230
do you calculate acceleration?

00:07:16.230 --> 00:07:18.480
And give you a little bit
of a sense of what it means.

00:07:18.480 --> 00:07:20.021
And once again, this
right here, when

00:07:20.021 --> 00:07:22.240
you have seconds squared in
the bottom of your units,

00:07:22.240 --> 00:07:23.531
it doesn't make a ton of sense.

00:07:23.531 --> 00:07:25.980
But we can rewrite
it like this up here.

00:07:25.980 --> 00:07:35.650
This is 1/180 miles per second.

00:07:35.650 --> 00:07:40.310
And then we divide by
seconds again, per second.

00:07:40.310 --> 00:07:43.550
Or maybe I can write
like this, per second,

00:07:43.550 --> 00:07:46.079
where this whole thing
is the numerator.

00:07:46.079 --> 00:07:47.620
So this makes a
little bit more sense

00:07:47.620 --> 00:07:49.410
from an acceleration
point of view.

00:07:49.410 --> 00:07:52.490
1/180 miles per
second, per second.

00:07:52.490 --> 00:07:55.400
Every second, this
Porsche 911 is

00:07:55.400 --> 00:08:01.400
going to go 1/180 of a
mile per second faster.

00:08:01.400 --> 00:08:03.150
And actually, it's
probably more intuitive

00:08:03.150 --> 00:08:05.483
to stick to the miles per
hour, because that's something

00:08:05.483 --> 00:08:07.720
that we have a little
bit more sense on.

00:08:07.720 --> 00:08:10.210
And another way to visualize it.

00:08:10.210 --> 00:08:12.960
If you were to be
driving that Porsche,

00:08:12.960 --> 00:08:15.580
and you were to look at the
speedometer for that Porsche,

00:08:15.580 --> 00:08:17.620
and if the acceleration
was constant--

00:08:17.620 --> 00:08:20.030
it's actually not going to
be completely constant--

00:08:20.030 --> 00:08:22.030
and if you look at
speedometer-- let me draw it.

00:08:22.030 --> 00:08:30.069
So this would be 10,
20, 30, 40, 50, 60.

00:08:30.069 --> 00:08:32.360
This is probably not what
the speedometer for a Porsche

00:08:32.360 --> 00:08:32.859
looks like.

00:08:32.859 --> 00:08:36.520
This is probably more analogous
to a small four cylinder car's

00:08:36.520 --> 00:08:37.530
speedometer.

00:08:37.530 --> 00:08:39.740
I suspect the Porsche's
speedometer goes much

00:08:39.740 --> 00:08:41.321
beyond 60 miles per hour.

00:08:41.321 --> 00:08:42.820
But what you would
see for something

00:08:42.820 --> 00:08:45.880
accelerating this fast is,
right when you're starting,

00:08:45.880 --> 00:08:48.080
the speedometer
would be right there.

00:08:48.080 --> 00:08:51.480
And that every second it would
be 20 miles per hour faster.

00:08:51.480 --> 00:08:53.700
So after a second
the speedometer

00:08:53.700 --> 00:08:54.810
would have moved this far.

00:08:54.810 --> 00:08:56.310
After another second
the speedometer

00:08:56.310 --> 00:08:57.436
would have moved this far.

00:08:57.436 --> 00:08:59.310
And then after another
second the speedometer

00:08:59.310 --> 00:09:01.081
would have moved that far.

00:09:01.081 --> 00:09:02.830
And the entire time
you would have kind of

00:09:02.830 --> 00:09:05.750
been pasted to the
back of your seat.


Gravity for astronauts in orbit

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:03.160
When you look at footage or
photographs of astronauts

00:00:03.160 --> 00:00:06.980
in space, it doesn't look like
there's any gravity at work

00:00:06.980 --> 00:00:07.510
here.

00:00:07.510 --> 00:00:10.080
Everything is not falling
down in one direction.

00:00:10.080 --> 00:00:12.810
In fact, it's not even
clear what up or down is.

00:00:12.810 --> 00:00:14.390
Everything just floats around.

00:00:14.390 --> 00:00:15.900
If I were to push
off of this wall,

00:00:15.900 --> 00:00:17.920
I would just float
in that direction.

00:00:17.920 --> 00:00:22.250
So it doesn't look like there's
this overarching influence

00:00:22.250 --> 00:00:26.550
like gravity that's trying
to pull everything down.

00:00:26.550 --> 00:00:29.760
But the question is that
these astronauts are still

00:00:29.760 --> 00:00:32.880
not too far away from
a supermassive body.

00:00:32.880 --> 00:00:36.190
In fact, the space shuttle
gets up only a couple

00:00:36.190 --> 00:00:38.834
of hundred miles above
the surface of the Earth.

00:00:38.834 --> 00:00:41.000
So the space shuttle, if I
were to draw it to scale,

00:00:41.000 --> 00:00:43.640
would probably be
right about there.

00:00:43.640 --> 00:00:47.680
And we know that the force of
gravity between two objects

00:00:47.680 --> 00:00:51.670
is equal to big G, the
gravitational constant, times

00:00:51.670 --> 00:00:55.000
the mass of the first
object, times the mass

00:00:55.000 --> 00:00:59.060
of the second object over
the distance between the two

00:00:59.060 --> 00:01:00.830
objects squared.

00:01:00.830 --> 00:01:02.550
And if the space
shuttle is right here,

00:01:02.550 --> 00:01:06.590
only a few hundred miles above
the surface of the Earth,

00:01:06.590 --> 00:01:08.570
this r isn't that different.

00:01:08.570 --> 00:01:10.515
It's a little bit
further than if you

00:01:10.515 --> 00:01:11.890
were at the surface
of the Earth.

00:01:11.890 --> 00:01:16.266
Remember that r is measured from
wherever you are to the center,

00:01:16.266 --> 00:01:17.890
from the center of
the Earth, or really

00:01:17.890 --> 00:01:20.100
the center of the object
to the center of the Earth.

00:01:20.100 --> 00:01:22.951
The center of the Earth
represents most of the distance

00:01:22.951 --> 00:01:23.450
here.

00:01:23.450 --> 00:01:25.230
So if I'm at the
surface of the Earth

00:01:25.230 --> 00:01:27.440
or if I'm just a few hundred
miles above the surface

00:01:27.440 --> 00:01:30.880
of the Earth, it's not going
to change r that dramatically,

00:01:30.880 --> 00:01:33.600
especially in terms
of percentage.

00:01:33.600 --> 00:01:35.870
So when you look at it this
way, it seems pretty clear

00:01:35.870 --> 00:01:38.760
that the force of
gravity for someone who

00:01:38.760 --> 00:01:42.050
is in space only a few
hundred miles above the Earth

00:01:42.050 --> 00:01:46.140
should not be that different
than the force of gravity

00:01:46.140 --> 00:01:48.900
for someone who is on
the surface of the Earth.

00:01:48.900 --> 00:01:51.540
So my question to
you is, what gives?

00:01:51.540 --> 00:01:53.960
If there should be
gravity in space,

00:01:53.960 --> 00:01:55.520
how can we see all
of these pictures

00:01:55.520 --> 00:01:58.660
of people floating
around like this?

00:01:58.660 --> 00:02:02.030
And the answer is that
there is gravity in space,

00:02:02.030 --> 00:02:05.150
and that these people
actually are falling.

00:02:05.150 --> 00:02:08.400
They're just moving fast
enough relative to the Earth

00:02:08.400 --> 00:02:09.709
that they keep missing it.

00:02:09.709 --> 00:02:11.750
And let me show you what
I'm talking about there.

00:02:16.220 --> 00:02:18.030
Let's say I'm sitting
here in Africa,

00:02:18.030 --> 00:02:20.760
and I were to shoot
something, if maybe I

00:02:20.760 --> 00:02:22.310
have a really good
sling shot, and I

00:02:22.310 --> 00:02:25.830
were to sling something super
fast and maybe at a 45 degree

00:02:25.830 --> 00:02:27.970
angle, it might take
off a little bit

00:02:27.970 --> 00:02:29.702
and eventually
hit another point.

00:02:29.702 --> 00:02:32.160
And this would actually already
be a super duper slingshot.

00:02:32.160 --> 00:02:34.860
I just made it travel a couple
of thousand miles or at least

00:02:34.860 --> 00:02:36.180
over 1,000 miles.

00:02:36.180 --> 00:02:38.120
If I make it go a
little bit faster,

00:02:38.120 --> 00:02:40.620
if I put a little
bit more force on,

00:02:40.620 --> 00:02:43.660
if I just propelled the
projectile a little bit faster,

00:02:43.660 --> 00:02:45.190
it might go a
little bit further,

00:02:45.190 --> 00:02:47.340
but it will eventually
fall back to the Earth.

00:02:47.340 --> 00:02:50.480
Let's try to propel it a
little bit faster than that.

00:02:50.480 --> 00:02:52.630
Then it'll still
fall to the Earth.

00:02:52.630 --> 00:02:54.920
Let's propel it even
faster than that.

00:02:54.920 --> 00:02:57.930
Well then, it's still eventually
going to fall to the Earth.

00:02:57.930 --> 00:02:59.680
I think you might see
where this is going.

00:02:59.680 --> 00:03:01.210
Let's go even faster than that.

00:03:01.210 --> 00:03:02.942
So if we go even
faster than that,

00:03:02.942 --> 00:03:04.400
eventually it'll
fall to the Earth.

00:03:04.400 --> 00:03:07.490
Even faster than
that, so if you were

00:03:07.490 --> 00:03:10.630
to throw an object
even faster than that,

00:03:10.630 --> 00:03:14.115
it would then go really far
and then fall to the Earth.

00:03:14.115 --> 00:03:15.490
I think you see
what's happening.

00:03:15.490 --> 00:03:17.810
Every time you go
faster and faster,

00:03:17.810 --> 00:03:20.640
you throw this projectile
faster and faster,

00:03:20.640 --> 00:03:24.070
it gets further and
further, up to some velocity

00:03:24.070 --> 00:03:27.540
that you release
this projectile,

00:03:27.540 --> 00:03:30.050
and whenever it's trying
to fall to the Earth,

00:03:30.050 --> 00:03:32.730
it's going so fast that it
keeps missing the Earth.

00:03:32.730 --> 00:03:36.710
So it'll keep going around and
around and around the Earth,

00:03:36.710 --> 00:03:40.910
and a projectile like that
would essentially be in orbit.

00:03:40.910 --> 00:03:42.380
So what's happening
is if there was

00:03:42.380 --> 00:03:46.140
no gravity for that projectile,
if there was no gravity,

00:03:46.140 --> 00:03:51.440
the projectile would just
go straight away into space.

00:03:51.440 --> 00:03:54.320
But because there's gravity,
it's constantly pulling it

00:03:54.320 --> 00:03:57.750
towards the center of
the Earth, or the center

00:03:57.750 --> 00:04:00.020
of that projectile and
the center of the Earth

00:04:00.020 --> 00:04:01.781
are being pulled
towards each other,

00:04:01.781 --> 00:04:03.530
I guess is a better
way to think about it.

00:04:03.530 --> 00:04:05.460
The force of gravity
is doing that.

00:04:05.460 --> 00:04:07.430
And so it's curving its path.

00:04:07.430 --> 00:04:10.450
And if it's going fast enough,
if the projectile or whatever

00:04:10.450 --> 00:04:12.450
object we're talking about
is going fast enough,

00:04:12.450 --> 00:04:15.700
it'll just keep going
round and round the Earth.

00:04:15.700 --> 00:04:20.190
And since there is almost,
pretty much, for most purposes

00:04:20.190 --> 00:04:24.190
no air if you go high enough,
especially the altitude

00:04:24.190 --> 00:04:28.050
that the space shuttle
is, no noticeable drag,

00:04:28.050 --> 00:04:29.900
this thing can
just keep on going

00:04:29.900 --> 00:04:31.370
for a substantial
amount of time.

00:04:31.370 --> 00:04:33.203
Although there is just
a little bit of drag,

00:04:33.203 --> 00:04:37.030
and that's why over time you
do have satellites slow down,

00:04:37.030 --> 00:04:39.740
because there is just a
little bit of air resistance.

00:04:39.740 --> 00:04:42.470
So the answer to
this conundrum is

00:04:42.470 --> 00:04:45.260
that there actually is gravity.

00:04:45.260 --> 00:04:47.410
It's not a gravity-free
environment.

00:04:47.410 --> 00:04:50.660
It's just that the astronauts
and the space shuttle

00:04:50.660 --> 00:04:52.760
and everything else that's
in the space shuttle,

00:04:52.760 --> 00:04:55.230
it's all falling,
but it's moving

00:04:55.230 --> 00:04:57.450
fast enough that it
never hits the Earth.

00:04:57.450 --> 00:04:58.770
It keeps missing the Earth.

00:04:58.770 --> 00:05:01.570
It keeps going round
and round and round,

00:05:01.570 --> 00:05:04.860
but it is completely under
the influence of gravity.

00:05:04.860 --> 00:05:07.470
If they were to just
slow themselves down,

00:05:07.470 --> 00:05:11.180
if they were to just brake
relative to the Earth,

00:05:11.180 --> 00:05:14.240
and if they were to just
put their brakes on right

00:05:14.240 --> 00:05:17.910
over there, they would all
just plummet to the Earth.

00:05:17.910 --> 00:05:21.600
So there's nothing special
about going 300 or 400 miles up

00:05:21.600 --> 00:05:24.500
into space, that all of a
sudden gravity disappears.

00:05:24.500 --> 00:05:26.580
The influence of gravity,
actually on some level,

00:05:26.580 --> 00:05:27.460
it just keeps going.

00:05:27.460 --> 00:05:29.660
You can't, it might
become unnoticeably

00:05:29.660 --> 00:05:31.849
small at some point,
but definitely

00:05:31.849 --> 00:05:33.890
for only a couple of
hundred miles up in the air,

00:05:33.890 --> 00:05:35.941
there is definitely
gravity there.

00:05:35.941 --> 00:05:38.190
It's just they're in orbit,
they're going fast enough.

00:05:38.190 --> 00:05:39.870
So if they just keep
falling, they're

00:05:39.870 --> 00:05:41.460
never going to hit the Earth.

00:05:41.460 --> 00:05:42.960
And if you want to
simulate gravity,

00:05:42.960 --> 00:05:45.970
and this is actually how
NASA does simulate gravity,

00:05:45.970 --> 00:05:47.980
is that they will put
people in a plane,

00:05:47.980 --> 00:05:49.960
and they call it
the vomit rocket

00:05:49.960 --> 00:05:51.920
because it's known
to make people sick,

00:05:51.920 --> 00:05:54.030
and they'll make them go
in a projectile motion.

00:05:54.030 --> 00:05:57.290
So if this is the ground,
in a projectile path

00:05:57.290 --> 00:05:59.700
or in a parabolic
path I should say,

00:05:59.700 --> 00:06:02.370
so the plane will
take off, and it

00:06:02.370 --> 00:06:07.800
will do a path exactly the
same as something in free fall

00:06:07.800 --> 00:06:09.520
or in a parabolic path.

00:06:09.520 --> 00:06:11.490
And so anyone who's
sitting in that plane

00:06:11.490 --> 00:06:13.570
will experience free fall.

00:06:13.570 --> 00:06:16.010
So if you've ever been
in, if you've ever right

00:06:16.010 --> 00:06:18.120
when you jump off of a
or if you've ever bungee

00:06:18.120 --> 00:06:21.850
jumped or skydived
or even the feeling

00:06:21.850 --> 00:06:23.940
when a roller coaster is
going right over the top,

00:06:23.940 --> 00:06:25.731
and it's pulling you
down, and your stomach

00:06:25.731 --> 00:06:28.780
feels a little ill, that
feeling of free fall, that's

00:06:28.780 --> 00:06:31.720
the exact same feeling
that these astronauts feel

00:06:31.720 --> 00:06:34.190
because they're in a
constant state of free fall.

00:06:34.190 --> 00:06:37.390
But that is an
indistinguishable feeling from,

00:06:37.390 --> 00:06:40.570
if you were just in deep space
and you weren't anywhere close

00:06:40.570 --> 00:06:45.740
any noticeable mass, that is
an identical feeling that you

00:06:45.740 --> 00:06:50.290
would feel to having no
gravitational force around you.

00:06:50.290 --> 00:06:52.335
So hopefully that clarifies
things a little bit.

00:06:52.335 --> 00:06:54.460
To someone who's just
sitting in the space shuttle,

00:06:54.460 --> 00:06:56.280
and if they had no
windows, there's

00:06:56.280 --> 00:06:58.020
no way of them
knowing whether they

00:06:58.020 --> 00:07:00.000
are close to a massive
object and they're just

00:07:00.000 --> 00:07:03.650
in free fall around it, they're
in orbit, or whether they're

00:07:03.650 --> 00:07:06.300
just completely far away
from any massive object,

00:07:06.300 --> 00:07:09.080
and they really are in
a state of or in a place

00:07:09.080 --> 00:07:11.275
where there's very
little gravity.


Introduction to gravity

WEBVTT
Kind: captions
Language: en

00:00:00.800 --> 00:00:08.667
Everything in human experience, and really human history or human civilizations experience, is that everything

00:00:08.667 --> 00:00:15.933
seems to fall to the earth, that if you have water particles, they don't just float up.

00:00:15.933 --> 00:00:16.433
If they are small enough they are being held up by the wind and all that, but if they are large enough, they will fall.

00:00:16.433 --> 00:00:25.733
That you don't have people that are able to just float around, they will fall.

00:00:25.733 --> 00:00:28.400
You don't have taxi cabs that float around, they'll fall.

00:00:28.400 --> 00:00:32.467
Not only will the water fall, it will hit the ground, it will puddle up, and if there is a gutter it

00:00:32.467 --> 00:00:38.200
will fall into the gutter. It is just trying to get lower and lower and lower.

00:00:38.200 --> 00:00:42.733
If i were to drop a bunch of needles they would just fall. They don't... If i had a needle at rest here

00:00:42.733 --> 00:00:49.333
it doesn't just automatically for no reason jump and fly upwards and start to float.

00:00:49.333 --> 00:00:53.667
And so it is just a thing that is fundamental to everything that we have ever

00:00:53.667 --> 00:00:55.933
ever experienced.

00:00:55.933 --> 00:01:03.333
And so, for most of human history or human civilization, we just accepted it as a given.

00:01:03.333 --> 00:01:10.133
We thought, "well look it's just obvious, everything should just fall down, that's just the way the universe is.

00:01:10.133 --> 00:01:18.933
To think otherwise would just be crazy." And that's why this guy, this guy right over here, is one of the greatest geniuses

00:01:18.933 --> 00:01:21.600
of all time. He did many more things than just the things I am going to describe in this video,

00:01:21.600 --> 00:01:24.867
and any one of those things would have earned him his place in history.

00:01:24.867 --> 00:01:31.667
And this, as you may already know, is Isaac Newton.

00:01:31.667 --> 00:01:38.467
Easily one of the top five minds in all of human history. So a pretty fascinating dude.

00:01:38.467 --> 00:01:43.236
And one of his big insights about this 'things falling down' problem is:

00:01:43.236 --> 00:01:45.041
Do they have to fall down?

00:01:45.041 --> 00:01:49.467
Is this just something we should assume about the universe?

00:01:49.467 --> 00:01:58.133
Things just need to fall down, he said, or we were told he said that he was somewhat inspired by

00:01:58.133 --> 00:02:05.000
observing an apple falling from a tree. It's probably not true that you'll see in some cartoons

00:02:05.000 --> 00:02:09.923
on television that the apple hit his head or hit his head while he was sleeping and gave him the idea.

00:02:09.923 --> 00:02:15.800
Most people were to see... Let me draw a tree here.

00:02:15.800 --> 00:02:30.333
That's a twig right there, some leaves. So if most people... So that is an apple over here.

00:02:30.333 --> 00:02:38.067
So if most people... If i were to snap this twig over here, the apple would fall. Pretty much common sense. The apple would fall.

00:02:38.067 --> 00:02:44.067
And if most people were to see that, they would just think it's a normal happening in the universe. But for Isaac Newton, at least on that day,

00:02:44.067 --> 00:02:50.600
he asked himself, "Why? Why did that apple fall?"

00:02:50.600 --> 00:02:54.267
And this, to some degree, is a great example of "out of the box" thinking, because something

00:02:54.267 --> 00:03:00.133
for thousands of years or tens of thousands of years human beings had taken for granted, just

00:03:00.133 --> 00:03:03.733
because that's the way it always was. He actually asked the question why?

00:03:03.733 --> 00:03:07.067
Does it always have to be that way?

00:03:07.067 --> 00:03:11.933
And that question took him down a entire line of reasoning that set up the basis for all of

00:03:11.933 --> 00:03:15.867
classical mechanics for the most part we still use today.

00:03:15.867 --> 00:03:20.733
It has been tweaked a good bit by this gentleman in the last hundred years. [Albert Einstein]

00:03:20.733 --> 00:03:26.067
But for most purposes, when we're engineering things on the surface of the planet,

00:03:26.067 --> 00:03:35.745
and we are not going close to the speed of light, we can still use the mathematics that Isaac Newton came up with from this simple question.

00:03:35.822 --> 00:03:39.939
And not only was he able to kind of think that there's something...

00:03:39.939 --> 00:03:42.912
There's something that might be pulling, somehow,

00:03:42.912 --> 00:03:45.930
acting on this apple, bringing it to the earth.

00:03:45.930 --> 00:03:49.599
But he actually formulated an entire, an entire.. I guess

00:03:49.599 --> 00:03:52.943
Law around this thing. So, as you can imagine,

00:03:52.943 --> 00:03:58.796
the thing that Isaac Newton believes brought the apple to the Earth

00:03:58.796 --> 00:04:00.710
is gravity... is gravity.

00:04:01.988 --> 00:04:05.311
And he formulated the universal Law of gravitation, or the law of universal gravitation; either way.

00:04:09.067 --> 00:04:14.267
And in it, he theorizes that the forces between objects

00:04:14.267 --> 00:04:17.733
now it's a vector quantity, it's always going to attract the two objects to each other.

00:04:17.733 --> 00:04:23.800
So the direction is towards each other. The force of gravity between two objects...

00:04:23.800 --> 00:04:33.000
is going to be equal to this this big G, which is really just a number, its a very small number.

00:04:33.000 --> 00:04:41.200
I'll give you that number in a second. It's equal to this constant, this gravitation constant.

00:04:41.200 --> 00:04:49.133
Which is a super-duper small number, times the mass of the first object, times the mass of the second

00:04:49.133 --> 00:04:57.800
object, divided by the distance between the two objects. Distance squared.

00:04:57.800 --> 00:05:09.067
So this is distance between two objects.

00:05:09.067 --> 00:05:14.333
So if you're talking about the force of gravity on Earth, this right over here...

00:05:14.333 --> 00:05:21.800
You pick one of the masses to be Earth, so this mass over here. You pick one to be Earth.

00:05:21.800 --> 00:05:29.200
This is the object on Earth. Maybe it's me. Then this is the distance between the center

00:05:29.200 --> 00:05:38.933
of masses between those two objects. The center of me and center of the Earth.

00:05:38.933 --> 00:05:42.467
So really it's from roughly the distance from the surface of the Earth or if I'm roughly

00:05:42.467 --> 00:05:47.000
five foot-nine [inches tall] then about half of that distance to the center of the Earth

00:05:47.000 --> 00:05:54.867
is this number right over here. So right when you see this, before we even talk about me and Earth,

00:05:54.867 --> 00:06:01.067
or needles and Earth, or taxi cabs and Earth and that force of gravity, you might have something

00:06:01.067 --> 00:06:07.867
bizarre raising up in your brain. You might be saying, "the way gravity is defined

00:06:07.867 --> 00:06:14.400
by Isaac Newton, this formula we're given right here, it's saying we have gravity between

00:06:14.400 --> 00:06:19.867
any two objects" and you're saying, "Look, I'm looking at a computer screen right now,

00:06:19.867 --> 00:06:30.200
so you're looking at a computer screen right now..." And let me draw an old school computer,

00:06:30.200 --> 00:06:36.800
not a flat panel. How come your not attracted to the computer screen?

00:06:36.800 --> 00:06:43.333
How come it doesn't fly into your face? And the answer there is, this number, this number is

00:06:43.333 --> 00:06:52.600
really small. And there actually is some force of attraction between you and the computer.

00:06:52.600 --> 00:07:00.067
It's just that it's more than overcompensated for the friction between the computer and the desk,

00:07:00.067 --> 00:07:06.067
the friction between you and your seat, which is frankly being caused by the force

00:07:06.067 --> 00:07:12.067
between you and the Earth, the force of gravitation between the computer and the Earth.

00:07:12.067 --> 00:07:17.333
That you and the computer have such small masses that you really can't notice it. It's really negligible.

00:07:17.333 --> 00:07:23.533
It's being overpowered by other forces that are keeping the computer from even drifting

00:07:23.533 --> 00:07:29.600
into your face or your face drifting into the computer. So just to get a sense of that...

00:07:29.600 --> 00:07:34.000
This G, this big G,

00:07:34.000 --> 00:07:38.733
this constant of proportionality, just to get a sense of how small it is... This is, and I'm going to round

00:07:38.733 --> 00:07:50.667
it here, it's approximately 6.67 times 10 to the negative 11th Newtons.

00:07:50.667 --> 00:07:53.667
And we'll talk about Newtons, it is the metric unit of force.

00:07:53.667 --> 00:08:09.200
Let me actually make sure I say this correctly. Newton meters per kilogram squared. Newton times meter per kilogram, squared.

00:08:09.200 --> 00:08:13.400
It's this strange set of units here, but the units are really there. So when you multiply by two masses,

00:08:13.400 --> 00:08:19.400
which are in kilograms, and divide by a distance, which is in meters, you'll end up with Newtons.

00:08:19.400 --> 00:08:22.933
But I want to make it clear that this is a super small number.

00:08:22.933 --> 00:08:29.000
Ten to the negative 11th. If I were to just write 10 to the negative 11th, it would be 0.0 and

00:08:29.000 --> 00:08:46.133
then we would have eleven 0's. So this number right here is the same as 6.67 times

00:08:46.133 --> 00:08:54.333
this thing over here. So this is a super small number. And that is why if you multipy it by not so

00:08:54.333 --> 00:08:57.733
large numbers, if you don't use Earth, if you use yourself and a computer,

00:08:57.733 --> 00:09:04.667
you're going to end up still with a super duper small force. Something so small that you won't

00:09:04.667 --> 00:09:08.133
notice it. It is going to be overpowered by other forces, so these things don't fly into each other.

00:09:08.133 --> 00:09:14.267
But when you think about really massive bodies, like the Earth, the force of gravity

00:09:14.267 --> 00:09:19.600
starts to become noticeable, very noticeable. And I'm not going to give you the mass of Earth in this

00:09:19.600 --> 00:09:25.733
video, you can look it up yourself. But if you put in the mass of Earth right over here,

00:09:25.733 --> 00:09:30.933
if you put it in right over there, and if you put in roughly the distance from the surface

00:09:30.933 --> 00:09:37.933
of the Earth to the center of the Earth for R, and you multiply that by G. All of these terms over here...

00:09:37.933 --> 00:09:44.600
So this term, if you multiply that times that term and multiply by this term squared,

00:09:44.600 --> 00:09:53.000
they simplify to what is sometimes called little g. Little g. So this right here, we can view that

00:09:53.000 --> 00:09:57.400
as the gravitational field at the surface of Earth. It's also the same thing as the acceleration

00:09:57.400 --> 00:10:03.933
of gravity at the surface of the Earth, and this, and once again I'm just going to round it

00:10:03.933 --> 00:10:09.867
for the sake... This is... This comes out to be, units wise, 9.8 meters per second squared.

00:10:09.867 --> 00:10:18.267
Then you're left with just the other mass. So times M1. So for simplicity, if something

00:10:18.267 --> 00:10:28.000
is close to the surface of the Earth, the distance does matter. We can say that the force of

00:10:28.000 --> 00:10:35.600
gravity can be this "little g" times whatever the mass is close to Earth. For example,

00:10:35.600 --> 00:10:44.933
if you were to take me, and I weighed 70 kilograms... So, in the case of Sal, Sal has a...Actually I

00:10:44.933 --> 00:10:51.400
shouldn't say weight, I have a mass of 70 kilograms. I have a mass of 70 kilograms.

00:10:51.400 --> 00:10:55.667
Weight is actually a force, but we'll talk about that, clarify that more later.

00:10:55.667 --> 00:11:03.733
My mass is 70 kilograms, then we can figure out the force that the Earth is pulling down on me

00:11:03.733 --> 00:11:10.733
which is actually my weight. So in this situation, the force is going to be g, which is 9.8 meters

00:11:10.733 --> 00:11:27.400
per second squared, times my mass, which is 70 kilograms. And let me get my handy T85 calculator

00:11:27.400 --> 00:11:42.067
out to figure this out. So I get 9.8 times 70. That gives me...686. So this is equal to 686

00:11:42.067 --> 00:11:53.400
kilogram meters per second squared. OR this is the exact same thing as this thing right over here.

00:11:53.400 --> 00:12:00.867
This IS the definition of a Newton. So this is a newton, which is appropriately named for

00:12:00.867 --> 00:12:04.000
the guy that is the Father of All Classical Physics.

00:12:04.000 --> 00:12:11.000
So my weight on Earth, which is the same thing as the force that Earth is pulling down on me,

00:12:11.000 --> 00:12:22.400
or that the gravitational attraction between the Earth and me is 686 newtons. Now I will ask you

00:12:22.400 --> 00:12:24.333
an interesting question.

00:12:24.333 --> 00:12:31.267
So here is Earth,

00:12:31.267 --> 00:12:33.867
and I am not even a speck of a speck on Earth, but say for simplicity let's say

00:12:33.867 --> 00:12:40.133
this is me, I'm hanging out in the Indian Ocean some place. So that is me.

00:12:40.133 --> 00:12:49.267
And we already know that Earth is pulling down on me with a force of 686 newtons.

00:12:49.267 --> 00:12:57.133
Now my question to you is, "Am I pulling on the Earth with any force? And am I pulling on the Earth with

00:12:57.133 --> 00:13:01.067
a larger or small force that is pulling on me?"

00:13:01.067 --> 00:13:08.200
And your gut or your knee-jerk reaction might be: Earth is so huge, Sal is so tiny.

00:13:08.200 --> 00:13:14.333
Clearly the Earth must be pulling with a greater force than Sal is pulling on the Earth.

00:13:14.333 --> 00:13:17.800
Unfortunately that is NOT the case.

00:13:17.800 --> 00:13:26.733
That I am. So the Earth is pulling on Sal with the force of 686 Newtons and Sal is also pulling on the

00:13:26.733 --> 00:13:34.067
Earth with a force of 686 Newtons. So Sal is also pulling on the Earth. It makes me feel very powerful

00:13:34.067 --> 00:13:39.333
with the force of 686 Newtons. But you might say, "Wait, that doesn't make sense, Sal."

00:13:39.333 --> 00:13:47.733
If I have a building over here, and if you were to, let's say, jump from the building, you're going to start...

00:13:47.733 --> 00:13:52.400
The force of gravity is going to be acting on you, and you're going to start accelerating downwards.

00:13:52.400 --> 00:13:57.333
It doesn't seem that the Earth is accelerating up to you. Wouldn't we notice that, every time someone

00:13:57.333 --> 00:14:03.067
were to jump off a building, that the Earth starting accelerating in a major way. And the way to think

00:14:03.067 --> 00:14:06.867
about that is that the force is the SAME. And we'll talk about that in other videos.

00:14:06.867 --> 00:14:17.400
Force is equal to mass times acceleration. So when we are talking about 686 Newtons, in terms of

00:14:17.400 --> 00:14:23.400
the force of Earth, the gravitational attraction between myself and Earth. And this is going to be

00:14:23.400 --> 00:14:30.467
68 kilograms, then this provides a pretty good acceleration on me. So in this case, if you

00:14:30.467 --> 00:14:39.600
solve for A... Solve for A over here. You're going to get 9.8 meters per second squared. Now, if you

00:14:39.600 --> 00:14:43.867
do the same thing for Earth... I already told you that we are pulling on each other with the same

00:14:43.867 --> 00:14:49.867
force, 686 Newtons. Now if you want to find out how much is the Earth accelerating... That force

00:14:49.867 --> 00:14:54.400
you're going to get a... I'm not even going to put it here. You're going to put a huge number

00:14:54.400 --> 00:15:04.000
in here. Huge number times the acceleration of Earth towards me. And since this is such a huge number,

00:15:04.000 --> 00:15:11.467
very very very large number, this is going to be an immeasurably small number, super small number.

00:15:11.467 --> 00:15:16.133
And frankly it's probably averaged out by the acceleration of Earth, or the force of gravity

00:15:16.133 --> 00:15:26.467
and all the other people and things on the surface of the planet. So it all averages out in the end.

00:15:26.467 --> 00:15:28.800
But even if it didn't, it would be negligible, you wouldn't even notice the acceleration of Earth

00:15:28.800 --> 00:15:36.533
towards me. But you would notice the acceleration of me towards Earth because of our vastly

00:15:36.533 --> 00:15:41.867
different masses. Even though we have the same force of attraction.


Displacement from time and velocity example

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:02.180
Let's do one more
example dealing

00:00:02.180 --> 00:00:05.120
with displacement,
velocity, and time.

00:00:05.120 --> 00:00:11.220
So we have if Marcia travels for
1 minute at 5 meters per second

00:00:11.220 --> 00:00:14.490
to the south, how much
will she be displaced?

00:00:20.120 --> 00:00:21.170
Let me do it this way.

00:00:21.170 --> 00:00:29.270
We know that velocity
is equal to displacement

00:00:29.270 --> 00:00:31.030
divided by time.

00:00:31.030 --> 00:00:33.490
And it's really, once
again, it is change in time.

00:00:33.490 --> 00:00:34.860
But we'll just say time.

00:00:34.860 --> 00:00:36.714
That's implicitly
change in time.

00:00:36.714 --> 00:00:38.380
And if you manipulate
this a little bit,

00:00:38.380 --> 00:00:41.390
you really just multiply
both sides by time.

00:00:41.390 --> 00:00:44.980
You just multiply both
sides by the variable t.

00:00:44.980 --> 00:00:46.309
You get displacement.

00:00:46.309 --> 00:00:47.350
Because this cancels out.

00:00:47.350 --> 00:00:49.100
You get displacement.

00:00:49.100 --> 00:00:52.420
And I'll flip this around.

00:00:52.420 --> 00:00:54.780
What's on the right-hand
side, I'll write on the left.

00:00:54.780 --> 00:00:57.730
So you get displacement
is equal to time

00:00:57.730 --> 00:01:00.120
times velocity or
velocity times time.

00:01:03.950 --> 00:01:06.970
Is equal to velocity times
time or velocity times

00:01:06.970 --> 00:01:08.450
change in time.

00:01:08.450 --> 00:01:11.000
So over here, they're
asking us for displacement.

00:01:11.000 --> 00:01:13.500
They're asking us how much
did Marcia get displaced?

00:01:13.500 --> 00:01:16.390
And they're saying that
she travels for 1 minute.

00:01:16.390 --> 00:01:18.894
So this 1 minute right over
here, this is her time.

00:01:18.894 --> 00:01:21.060
Sometimes you could view
that as her change in time.

00:01:21.060 --> 00:01:23.660
Or it really is
her change in time.

00:01:23.660 --> 00:01:27.150
If it said 0 minutes on her
stopwatch when she started,

00:01:27.150 --> 00:01:28.400
at the end it'll say 1 minute.

00:01:28.400 --> 00:01:30.170
Or if it said 5
minutes, if maybe it

00:01:30.170 --> 00:01:32.330
was 3:05 when she
started, it would be 3:06

00:01:32.330 --> 00:01:33.080
when she finished.

00:01:33.080 --> 00:01:34.712
So it was really
the change in time.

00:01:34.712 --> 00:01:36.420
Once again, I won't
write the delta there

00:01:36.420 --> 00:01:40.446
just because this is the way
you most frequently see it.

00:01:40.446 --> 00:01:41.820
But I want to tell
you that these

00:01:41.820 --> 00:01:44.560
are the same thing for the
purpose of this problem

00:01:44.560 --> 00:01:46.790
because sometimes you'll
see the delta there.

00:01:46.790 --> 00:01:50.940
So the 1 minute, so the t
right over here is 1 minute.

00:01:53.510 --> 00:01:56.030
At 5 meters per
second to the south.

00:01:59.700 --> 00:02:02.450
This right over here
is the velocity.

00:02:02.450 --> 00:02:05.820
They give us the magnitude,
which is 5 meters per second.

00:02:05.820 --> 00:02:07.330
Or you could say
that's the speed.

00:02:07.330 --> 00:02:10.610
And they also give us the
direction, to the south.

00:02:10.610 --> 00:02:19.860
So this right over here is 5
meters per second to the south.

00:02:19.860 --> 00:02:22.810
So we might just say, look, if
we want displacement, that's

00:02:22.810 --> 00:02:33.190
just going to be equal to 5
meters per second to the south

00:02:33.190 --> 00:02:34.630
times 1 minute.

00:02:40.100 --> 00:02:41.915
The problem here
is that when we're

00:02:41.915 --> 00:02:43.290
talking about
displacement, we're

00:02:43.290 --> 00:02:46.180
going to think about a magnitude
of how much it's moved.

00:02:46.180 --> 00:02:48.360
So it'll be a
distance of some kind.

00:02:48.360 --> 00:02:49.220
And some direction.

00:02:49.220 --> 00:02:50.890
We have our direction
here, but we

00:02:50.890 --> 00:02:52.786
don't want any
other units there.

00:02:52.786 --> 00:02:54.410
And if we just multiply
this over here,

00:02:54.410 --> 00:02:55.966
we have 1 minute over here.

00:02:55.966 --> 00:02:57.590
But we have seconds
in the denominator.

00:02:57.590 --> 00:02:59.360
You can't just cancel out
a minute and a second.

00:02:59.360 --> 00:03:00.000
So you can't just
say that you're

00:03:00.000 --> 00:03:02.430
going to get 5 and have
some weird thing here.

00:03:02.430 --> 00:03:03.900
So in order for it
to all work out,

00:03:03.900 --> 00:03:07.310
you have to either convert
the 5 meters per second to 5

00:03:07.310 --> 00:03:08.590
meters per minute.

00:03:08.590 --> 00:03:10.580
Or let me phrase
that another way.

00:03:10.580 --> 00:03:12.470
You have to convert
the 5 meters per second

00:03:12.470 --> 00:03:14.520
to some amount of
meters per minute,

00:03:14.520 --> 00:03:15.530
not 5 meters per minute.

00:03:15.530 --> 00:03:16.654
It's going to be different.

00:03:16.654 --> 00:03:19.560
Or you convert the
1 minute to seconds.

00:03:19.560 --> 00:03:21.260
So at least in my
mind, it's easier

00:03:21.260 --> 00:03:23.450
to convert 1 minute to seconds.

00:03:23.450 --> 00:03:25.120
So let's do that.

00:03:25.120 --> 00:03:26.230
So this is the same thing.

00:03:26.230 --> 00:03:28.679
1 minute times.

00:03:28.679 --> 00:03:30.220
And we want to get
rid of the minute.

00:03:30.220 --> 00:03:32.350
And the minute is essentially
in the numerator right now.

00:03:32.350 --> 00:03:33.470
We could put this over 1.

00:03:33.470 --> 00:03:34.550
But it's essentially
in the numerator.

00:03:34.550 --> 00:03:35.883
So we want to divide by minutes.

00:03:38.260 --> 00:03:40.790
And we want to
multiply by seconds.

00:03:40.790 --> 00:03:43.290
We want seconds
in the numerator.

00:03:43.290 --> 00:03:46.210
And so how many seconds
are there per minute?

00:03:46.210 --> 00:03:50.602
You have 60 seconds
for every 1 minute.

00:03:50.602 --> 00:03:52.435
And so you have a minute
cancelling out with

00:03:52.435 --> 00:03:53.380
the minutes.

00:03:53.380 --> 00:03:55.060
And so now you have
5 meters per second

00:03:55.060 --> 00:03:56.950
to the south times 60 seconds.

00:03:56.950 --> 00:04:00.170
This is now cool because you
have seconds and seconds.

00:04:00.170 --> 00:04:03.020
I wrote "sec" there,
but this is also sec.

00:04:03.020 --> 00:04:06.520
So now you have
seconds over seconds.

00:04:06.520 --> 00:04:07.850
Those cancel out.

00:04:07.850 --> 00:04:09.730
And so your
displacement is going

00:04:09.730 --> 00:04:13.820
to be equal to 5 times 60.

00:04:17.970 --> 00:04:20.779
And then your units
left are meters.

00:04:20.779 --> 00:04:23.210
All the time units have
cancelled out and then

00:04:23.210 --> 00:04:25.410
it's meters to the south.

00:04:25.410 --> 00:04:30.870
So meters to the south.

00:04:30.870 --> 00:04:41.100
And this is equal to 5 times
60 is 300 meters to the south.

00:04:41.100 --> 00:04:42.690
And we are done.

00:04:42.690 --> 00:04:44.840
That's how much she
has been displaced.

00:04:44.840 --> 00:04:46.470
If they just wanted
the distance,

00:04:46.470 --> 00:04:51.380
you could say that she
traveled 300 meters.

00:04:51.380 --> 00:04:52.110
Just that part.

00:04:52.110 --> 00:04:54.250
The magnitude of
the displacement,

00:04:54.250 --> 00:04:59.700
that is the distance
that she traveled.


Solving for time

WEBVTT
Kind: captions
Language: en

00:00:00.610 --> 00:00:03.450
Let's work through another
few scenarios involving

00:00:03.450 --> 00:00:06.860
displacement, velocity, and
time, or distance, rate,

00:00:06.860 --> 00:00:08.050
and time.

00:00:08.050 --> 00:00:12.450
So over here we have, Ben is
running at a constant velocity

00:00:12.450 --> 00:00:16.370
of three 3 meters per
second to the east.

00:00:19.600 --> 00:00:21.940
And just as a review,
this is a vector quantity.

00:00:21.940 --> 00:00:25.170
They're giving us the
magnitude and the direction.

00:00:25.170 --> 00:00:27.490
If they just said 3
meters per second,

00:00:27.490 --> 00:00:29.550
then that would just be speed.

00:00:29.550 --> 00:00:35.050
So this is the magnitude,
is 3 meters per second.

00:00:35.050 --> 00:00:36.480
And it is to the east.

00:00:36.480 --> 00:00:38.630
So they are giving
us the direction.

00:00:38.630 --> 00:00:40.620
So this is a vector quantity.

00:00:40.620 --> 00:00:43.090
And that's why it's
velocity instead of speed.

00:00:43.090 --> 00:00:51.400
How long will it take
him to travel 720 meters.

00:00:51.400 --> 00:00:53.820
So let's just remind
ourselves a few things.

00:00:53.820 --> 00:00:56.389
And I'll do it both with
the vector version of it.

00:00:56.389 --> 00:00:58.180
And maybe they should
say, how long will it

00:00:58.180 --> 00:01:03.660
take them to travel
720 meters to the east,

00:01:03.660 --> 00:01:07.599
to make sure, to make it clear,
that it is a vector quantity.

00:01:07.599 --> 00:01:09.890
So that it's displacement,
as opposed to just distance,

00:01:09.890 --> 00:01:11.570
but we'll do it both ways.

00:01:11.570 --> 00:01:14.250
So one way to think about it, if
we think about just the scalar

00:01:14.250 --> 00:01:18.750
version of it, we said
already that rate or speed

00:01:18.750 --> 00:01:25.060
is equal to the distance that
you travel over some time.

00:01:25.060 --> 00:01:26.420
I might write t there.

00:01:26.420 --> 00:01:27.960
But it's really
a change in time.

00:01:27.960 --> 00:01:30.251
So sometimes some people
would write a little triangle,

00:01:30.251 --> 00:01:32.340
a delta there, which
means change in time.

00:01:32.340 --> 00:01:34.280
But that's implicitly
meant when you just

00:01:34.280 --> 00:01:36.950
write over time like that.

00:01:36.950 --> 00:01:40.420
So rate or speed is equal
to distance divided by time.

00:01:40.420 --> 00:01:43.086
Now, if you know-- they're
giving us in this problem,

00:01:43.086 --> 00:01:44.210
they're giving us the rate.

00:01:44.210 --> 00:01:47.460
If we think about the
scalar part of it,

00:01:47.460 --> 00:01:51.480
they're telling us that
that is 3 meters per second.

00:01:51.480 --> 00:01:53.759
And they're also
telling us the time.

00:01:53.759 --> 00:01:55.550
Or, sorry, they're not
telling us the time.

00:01:55.550 --> 00:01:57.340
They are telling
us the distance,

00:01:57.340 --> 00:01:59.580
and they want us to
figure out the time.

00:01:59.580 --> 00:02:02.075
So they tell us the
distance is 720 meters.

00:02:06.680 --> 00:02:08.870
And so we just have to
figure out the time.

00:02:08.870 --> 00:02:11.699
we So if we just do the
scalar version of it,

00:02:11.699 --> 00:02:13.740
we're not dealing with
velocity and displacement.

00:02:13.740 --> 00:02:16.650
We're dealing with the
rate or speed and distance.

00:02:16.650 --> 00:02:19.560
So we have 3 meters
per second is

00:02:19.560 --> 00:02:28.857
equal to 720 meters over
some change in time.

00:02:28.857 --> 00:02:30.690
And so we can algebraically
manipulate this.

00:02:30.690 --> 00:02:32.850
We can multiply both
sides times time.

00:02:37.910 --> 00:02:40.240
Multiply time right over there.

00:02:40.240 --> 00:02:42.697
And then we could,
if we all-- well,

00:02:42.697 --> 00:02:44.280
let's just take it
one step at a time.

00:02:44.280 --> 00:03:00.490
So 3 meters per second times
time is equal to 720 meters

00:03:00.490 --> 00:03:02.930
because the times on the
right will cancel out

00:03:02.930 --> 00:03:03.990
right over there.

00:03:03.990 --> 00:03:06.800
And that makes sense,
at least units-wise,

00:03:06.800 --> 00:03:08.480
because time is going
to be in seconds,

00:03:08.480 --> 00:03:10.620
seconds cancel out the
seconds in the denominator,

00:03:10.620 --> 00:03:11.710
so you'll just get meters.

00:03:11.710 --> 00:03:13.226
So that just makes sense there.

00:03:13.226 --> 00:03:14.600
So if you want to
solve for time,

00:03:14.600 --> 00:03:17.210
you can divide both sides
by 3 meters per second.

00:03:24.324 --> 00:03:25.990
And then the left
side, they cancel out.

00:03:25.990 --> 00:03:28.320
On the right hand
side, this is going

00:03:28.320 --> 00:03:37.170
to be equal to 720
divided by 3 times meters.

00:03:37.170 --> 00:03:38.670
That's meters in the numerator.

00:03:38.670 --> 00:03:40.870
And you had meters per
second in the denominator.

00:03:40.870 --> 00:03:42.520
If you bring it out
to the numerator,

00:03:42.520 --> 00:03:43.750
you take the inverse of this.

00:03:43.750 --> 00:03:46.840
So that's meters-- let me do
the meters that was on top,

00:03:46.840 --> 00:03:47.840
let me do that in green.

00:03:47.840 --> 00:03:48.715
Let me color code it.

00:03:48.715 --> 00:03:50.570
So 720 meters.

00:03:50.570 --> 00:03:52.520
And now you're dividing
by meters per second.

00:03:52.520 --> 00:03:54.020
That's the same
thing as multiplying

00:03:54.020 --> 00:03:57.649
by the inverse, times
seconds per meters.

00:03:57.649 --> 00:03:59.190
And so what you're
going to get here,

00:03:59.190 --> 00:04:00.648
the meters are
going to cancel out,

00:04:00.648 --> 00:04:04.770
and you'll get 720
divided by 3 seconds.

00:04:04.770 --> 00:04:05.890
So what is that?

00:04:05.890 --> 00:04:07.650
720 divided by 3.

00:04:07.650 --> 00:04:09.650
72 divided by 3 is 24.

00:04:09.650 --> 00:04:12.230
So this is going to be 240.

00:04:12.230 --> 00:04:15.010
This part right over
here is going to be 240.

00:04:15.010 --> 00:04:18.339
And it's going to
be 240 seconds.

00:04:18.339 --> 00:04:20.230
That's the only unit
we're left with,

00:04:20.230 --> 00:04:24.670
and on the left hand side,
we just had the time.

00:04:24.670 --> 00:04:28.700
So the time is 240 seconds.

00:04:28.700 --> 00:04:30.214
Sometimes you'll see it.

00:04:30.214 --> 00:04:32.130
And just to show you,
in some physics classes,

00:04:32.130 --> 00:04:33.090
they'll show you
all these formulas.

00:04:33.090 --> 00:04:34.964
But one thing I really
want you to understand

00:04:34.964 --> 00:04:37.380
as we go through this
journey together,

00:04:37.380 --> 00:04:39.050
is that all of those
formulas are really

00:04:39.050 --> 00:04:41.500
just algebraic
manipulations of each other.

00:04:41.500 --> 00:04:43.700
So you really shouldn't
memorize any of them.

00:04:43.700 --> 00:04:45.325
You should always
say, hey, that's just

00:04:45.325 --> 00:04:48.080
manipulating one of those other
formulas that I got before.

00:04:48.080 --> 00:04:50.500
And even these formulas are,
hopefully, reasonably common

00:04:50.500 --> 00:04:51.000
sense.

00:04:51.000 --> 00:04:53.166
And so you can start from
very common sense things--

00:04:53.166 --> 00:04:55.100
rate is distance
divided by time--

00:04:55.100 --> 00:04:56.660
and then just
manipulate it to get

00:04:56.660 --> 00:04:58.911
other hopefully
common sense things.

00:04:58.911 --> 00:05:00.160
So we could have done it here.

00:05:00.160 --> 00:05:02.470
So we could have multiplied
both sides by time

00:05:02.470 --> 00:05:04.400
before we even put
in the variables,

00:05:04.400 --> 00:05:06.540
and you would have gotten--
So if you multiplied

00:05:06.540 --> 00:05:12.100
both sides by time here,
you would have got,

00:05:12.100 --> 00:05:16.400
on the right hand side, distance
is equal to time times rate,

00:05:16.400 --> 00:05:18.370
or rate times time.

00:05:18.370 --> 00:05:20.250
And this is one
of-- you'll often

00:05:20.250 --> 00:05:23.350
see this as kind of
the formula for rate,

00:05:23.350 --> 00:05:24.740
or the formula for motion.

00:05:24.740 --> 00:05:28.030
So if we flip it around, you get
distance is equal to rate times

00:05:28.030 --> 00:05:28.780
time.

00:05:28.780 --> 00:05:30.652
So these are all
saying the same things.

00:05:30.652 --> 00:05:32.360
And then if you wanted
to solve for time,

00:05:32.360 --> 00:05:35.290
you could divide
both sides by rate,

00:05:35.290 --> 00:05:39.020
and you get distance divided
by rate is equal to time.

00:05:39.020 --> 00:05:40.720
And that's exactly what we got.

00:05:40.720 --> 00:05:44.240
Distance divided by
rate was equal to time.

00:05:44.240 --> 00:05:46.150
So if your distance
is 720 meters,

00:05:46.150 --> 00:05:47.800
your rate is 3
meters per second,

00:05:47.800 --> 00:05:50.090
720 meters divided by
3 meters per second

00:05:50.090 --> 00:05:53.350
will also give you a
time of 240 seconds.

00:05:53.350 --> 00:05:55.240
If we wanted to do
the exact same thing,

00:05:55.240 --> 00:05:57.705
but the vector version
of it, just the notation

00:05:57.705 --> 00:05:59.080
will look a little
bit different.

00:05:59.080 --> 00:06:03.050
And we want to keep track
of the actual direction.

00:06:03.050 --> 00:06:08.000
So we could say we
know that velocity--

00:06:08.000 --> 00:06:10.870
and it is a vector quantity,
so I put a little arrow on top.

00:06:10.870 --> 00:06:15.320
Velocity is the same
thing as displacement.

00:06:15.320 --> 00:06:17.890
Let me pick a nice color
for displacement-- blue.

00:06:17.890 --> 00:06:21.230
As displacement-- Now, remember,
we use s for displacement.

00:06:21.230 --> 00:06:23.179
We don't want to
use d because when

00:06:23.179 --> 00:06:24.970
you start doing calculus,
especially vector

00:06:24.970 --> 00:06:26.680
calculus-- well, any
type of calculus--

00:06:26.680 --> 00:06:28.275
you use d for the
derivative operator.

00:06:28.275 --> 00:06:30.900
If you don't know what that is,
don't worry about it right now.

00:06:30.900 --> 00:06:32.695
But this right here,
s is displacement.

00:06:35.330 --> 00:06:36.620
At least this is convention.

00:06:36.620 --> 00:06:38.020
You could kind of use
anything, but this

00:06:38.020 --> 00:06:39.020
is what most people use.

00:06:39.020 --> 00:06:39.980
So if you don't want
to get confused,

00:06:39.980 --> 00:06:42.146
or if you don't want to be
confused when they use s,

00:06:42.146 --> 00:06:44.290
it's good to practice with it.

00:06:44.290 --> 00:06:46.510
So it's the
displacement per time.

00:06:46.510 --> 00:06:48.690
So it's displacement
divided by time.

00:06:48.690 --> 00:06:50.920
Sometimes, once again,
you'll have displacement

00:06:50.920 --> 00:06:52.910
per change in time,
which is really

00:06:52.910 --> 00:06:54.342
a little bit more correct.

00:06:54.342 --> 00:06:56.050
But I'll just go with
the time right here

00:06:56.050 --> 00:06:58.690
because this is the convention
that you see, at least in most

00:06:58.690 --> 00:07:00.590
beginning physics books.

00:07:00.590 --> 00:07:02.580
So once again, if we
want to solve for time,

00:07:02.580 --> 00:07:05.100
you can multiply
both sides by time.

00:07:05.100 --> 00:07:09.904
And you get-- this cancels
out-- and I'll flip this around.

00:07:09.904 --> 00:07:11.570
Well, actually, I'll
leave it like this.

00:07:11.570 --> 00:07:17.050
So you get displacement
is equal to-- I

00:07:17.050 --> 00:07:22.579
can flip these around--
velocity times change in time,

00:07:22.579 --> 00:07:23.120
I should say.

00:07:23.120 --> 00:07:25.328
Or we could just say time
just to keep things simple.

00:07:25.328 --> 00:07:26.820
And if you want
to solve for time,

00:07:26.820 --> 00:07:28.375
you divide both
sides by velocity.

00:07:32.430 --> 00:07:35.750
And then that gives you time
is equal to displacement

00:07:35.750 --> 00:07:37.629
divided by velocity.

00:07:37.629 --> 00:07:39.670
And so we can apply that
to this right over here.

00:07:39.670 --> 00:07:43.070
Our displacement is
720 meters to the east.

00:07:43.070 --> 00:07:47.990
So in this case, our time
is equal to 720 meters

00:07:47.990 --> 00:07:49.190
to the east.

00:07:49.190 --> 00:07:53.980
720 meters east is
our displacement,

00:07:53.980 --> 00:07:57.140
and we want to divide that
by the given velocity.

00:07:57.140 --> 00:07:59.310
Well, they give us the
velocity of 3 meters

00:07:59.310 --> 00:08:00.610
per second per the east.

00:08:04.140 --> 00:08:12.470
And once again, 720 divided
by 3 will give you 240.

00:08:12.470 --> 00:08:15.885
And then when you take
meters in the numerator,

00:08:15.885 --> 00:08:17.343
and you divide by
meters per second

00:08:17.343 --> 00:08:19.676
in the denominator, that's
the same thing as multiplying

00:08:19.676 --> 00:08:21.790
by seconds per meter,
those cancel out.

00:08:21.790 --> 00:08:24.440
And you are just left
with seconds here.

00:08:24.440 --> 00:08:25.860
One note I want to give you.

00:08:25.860 --> 00:08:28.650
In the last few problems, I've
been making vector quantities

00:08:28.650 --> 00:08:30.993
by saying to the
east, or going north.

00:08:30.993 --> 00:08:32.409
And what you're
going to see as we

00:08:32.409 --> 00:08:35.130
go into more complex problems--
and this is what you might see

00:08:35.130 --> 00:08:37.730
in typical physics
classes, or typical books,

00:08:37.730 --> 00:08:39.440
is that you define a convention.

00:08:39.440 --> 00:08:42.570
That maybe you'll say, the
positive direction, especially

00:08:42.570 --> 00:08:45.660
when we're just dealing
with one dimension,

00:08:45.660 --> 00:08:48.500
whether you can either
go forward or backwards,

00:08:48.500 --> 00:08:49.684
or left or right.

00:08:49.684 --> 00:08:51.350
We'll talk about other
vector quantities

00:08:51.350 --> 00:08:53.280
when we can move in two
or three dimensions.

00:08:53.280 --> 00:08:55.210
But they might take
some convention,

00:08:55.210 --> 00:09:00.780
like positive means maybe
you're moving to the east,

00:09:00.780 --> 00:09:04.890
and maybe negative means
you're moving to the west.

00:09:04.890 --> 00:09:09.220
And so that way-- well,
in the future, we'll see,

00:09:09.220 --> 00:09:10.610
the math will
produce the results

00:09:10.610 --> 00:09:11.960
that we see a little bit better.

00:09:11.960 --> 00:09:15.140
So this would just be
a positive 720 meters.

00:09:15.140 --> 00:09:17.787
This would be a positive
3 meters per second.

00:09:17.787 --> 00:09:19.870
And that implicitly tells
us that that's the east.

00:09:19.870 --> 00:09:21.820
If it was negative, it
would then be to the west.

00:09:21.820 --> 00:09:22.770
Something to think about.

00:09:22.770 --> 00:09:24.978
We're going to start exploring
that a little bit more

00:09:24.978 --> 00:09:26.220
in future videos.

00:09:26.220 --> 00:09:28.889
And maybe we might say positive
is up, negative is down,

00:09:28.889 --> 00:09:29.430
or who knows.

00:09:29.430 --> 00:09:30.888
There's different
ways to define it

00:09:30.888 --> 00:09:34.590
when you're dealing
in one dimension.