# An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 120 KJ to  72 KJ over t in [0, 4 s]. What is the average speed of the object?

Jan 28, 2017

Average speed is $177.46$ $\frac{m}{s}$.

#### Explanation:

As one Joule is equal to $1$ $k g {m}^{2} / {s}^{2}$ and as such the object's kinetic energy changes from $120 , 000 K J$ to $72000 K J$.

As kinetic energy $K E$ is given by $\frac{1}{2} m {v}^{2}$, velocity is given by $\sqrt{\frac{2 K E}{m}}$

and initial velocity is $\sqrt{\frac{2 \times 120000}{6}} = \sqrt{40000} = 200$ $\frac{m}{s}$

and final velocity is $\sqrt{\frac{2 \times 72000}{6}} = \sqrt{24000} = 154.92$ $\frac{m}{s}$

and average speed is $\frac{200 + 154.92}{2} = \frac{354.92}{2} = 177.46$ $\frac{m}{s}$.