# An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 54 KJ to 150 KJ over t in [0, 8 s]. What is the average speed of the object?

May 30, 2016

$\sqrt{2}$

#### Explanation:

Kinetic energy is given by the equation $K E = \frac{1}{2} m {v}^{2}$ where $m$ is the mass and $v$ is the velocity (speed)

The starting condition is $54 = \frac{1}{2} \cdot 6 {v}_{s}^{2}$
$\therefore {v}_{s}^{2} = 18$

${v}_{s} = 3 \sqrt{2}$

The end condition is $150 = \frac{1}{2} \cdot 6 {v}_{e}^{2}$

${v}_{e}^{2} = 50$

${v}_{e} = 5 \sqrt{2}$

The average speed is $\frac{{v}_{e} - {v}_{s}}{2}$

$\frac{5 \sqrt{2} - 3 \sqrt{2}}{2} = \frac{2 \sqrt{2}}{2} = \sqrt{2}$ k/s