# An object has a mass of 4 kg. The object's kinetic energy uniformly changes from 48 KJ to  320 KJ over t in [0, 12 s]. What is the average speed of the object?

Jan 15, 2017

Average speed is $227.46$ $\frac{m}{s}$

#### Explanation:

Kinetic energy of an objeect of mass $m$ kg. moving with a velocity of $v$ $\frac{m}{s}$ is given by $\frac{1}{2} m {v}^{2}$ joules. Let the initial velocity is $u$ and final velocity be $v$.

As the mass of the object is $4$ $k g .$ and initial kinetic energy is $48 K J$ or $48000 J$

We have $\frac{1}{2} \times 4 \times {u}^{2} = 48000$ i.e. ${u}^{2} = 24000$ and $u = \sqrt{24000} = \sqrt{{40}^{2} \times 15} = 40 \sqrt{15} = 154.92$ $\frac{m}{s}$

and as the mass of the object is $4$ $k g .$ and final kinetic energy is $320 K J$ or $320000 J$

$\frac{1}{2} \times 4 \times {u}^{2} = 320000$ i.e. ${u}^{2} = 160000$ and

$v = \sqrt{160000} = 400$ $\frac{m}{s}$

Hence average speed is $\frac{v + u}{2} = \frac{400 + 154.92}{2} = \frac{554.92}{2} = 227.46$ $\frac{m}{s}$