# An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 120 KJ to  36 KJ over t in [0, 4 s]. What is the average speed of the object?

May 18, 2016

$\overline{v} = 159.178$
Calling ${t}_{1} = 0 , {t}_{2} = 4 , {E}_{1} = 120000 , {E}_{2} = 36000 , m = 6$
interpolating the kinetic energy $e$ we get
$e = {E}_{1} + \left(\frac{{E}_{2} - {E}_{1}}{{t}_{2} - {t}_{1}}\right) \left(t - {t}_{1}\right)$ but $e = \frac{1}{2} m {v}^{2}$
$v = \sqrt{2 \frac{e}{m}}$. Average speed is obtained calculating
$\overline{v} = \frac{{\int}_{{t}_{1}}^{{t}_{2}} v \mathrm{dt}}{{t}_{2} - {t}_{1}} = 159.178$