# A car is traveling with a velocity of 30 m/s has a kinetic energy of 800,000 J. What is the mass of the car?

Dec 18, 2015

The mass of the car is 1800 kg.

#### Explanation:

Kinetic energy is the energy of motion. Anything that has motion has kinetic energy.

The equation for determining kinetic energy is $\text{KE} = \frac{1}{2} m {v}^{2}$, where $\text{KE}$ is kinetic energy in J, $m$ is mass in kg, and $v$ is speed in m/s.

Given
${\text{KE=800000 J"="800000 kg·m"^2/"s}}^{2}$
$v = \text{30 m/s}$

Unknown
$m$

Solution
Rearrange the equation to isolate $m$ and solve.

$\text{KE} = \frac{1}{2} m {v}^{2}$

$m = \frac{2 \text{KE}}{{v}^{2}}$

m=(2·800000"kg·m"^2/"s"^2)/((30"m/s")^2"

m=(2·800000"kg·m"^2/"s"^2)/(900"m"^2/"s"^2)

$m = \text{1800kg}$ (rounded to two significant figures)