# An object with a mass of 4 kg is acted on by two forces. The first is F_1= < 3 N , 2 N> and the second is F_2 = < 7 N, 6 N>. What is the object's rate and direction of acceleration?

Dec 21, 2016

The answer is $= 3.2 m {s}^{- 2}$ at 38.7º

#### Explanation:

The resulting force is

$\vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2}$

vecF=〈3,2〉+〈7,6〉=〈10,8〉

The magnitude of $\vec{F}$ is

=∥vecF∥ =∥〈10,8〉∥=sqrt(100+64)=sqrt164N

The rate of acceleration is =(∥vecF∥ )/m

$= \frac{\sqrt{164}}{4} = \frac{\sqrt{41}}{2} = 3.2 m {s}^{- 2}$

The direction is =arctan(8/10)=38.7º