# Question 3c3a8

Aug 1, 2017

$520$ $\text{kJ}$

#### Explanation:

The formula for kinetic energy is ${E}_{\text{K}} = \frac{1}{2} m {v}^{2}$; where $m$ is the mass of an object and $v$ is its velocity.

Let's substitute the given values into the formula:

$R i g h t a r r o w {E}_{\text{K}} = \frac{1}{2} \cdot 1612$ "kg" cdot (95.4 " km/h")^(2)

First, let's express the units $95.4$ $\text{km/h}$ in terms of ${\text{m s}}^{- 1}$:

$R i g h t a r r o w {E}_{\text{K}} = 806$ "kg" cdot (95.4 cdot frac(1000)(3600) "m s"^(- 1))^(2)#

$R i g h t a r r o w {E}_{\text{K}} = 806$ $\text{kg} \cdot 645.16$ ${\text{m"^(2) cdot "s}}^{- 2}$

$R i g h t a r r o w {E}_{\text{K}} = 519 , 998.96$ ${\text{kg" cdot "m"^(2) cdot "s}}^{- 2}$

Then, let's express this kinetic energy in joules:

$R i g h t a r r o w {E}_{\text{K}} = 519 , 998.96$ $\text{J}$

Now, we must express the kinetic energy in kilojoules.

So let's divide the value by ${10}^{3}$:

$R i g h t a r r o w {E}_{\text{K}} = \frac{519 , 998.96}{{10}^{3}}$ $\text{kJ}$

$\therefore {E}_{\text{K}} = 519.99896$ $\text{kJ}$

Therefore, the kinetic energy of this vehicle is around $520$ $\text{kJ}$.