What is the average speed of an object that is moving at 30 m/s at t=0 and accelerates at a rate of a(t) =5-2t^2 on t in [0,5]?

Feb 10, 2016

$V = - 28 , 3 \frac{m}{s}$

Explanation:

$v = \int a \cdot d t$
$v = {\int}_{0}^{5} \left(5 - 2 {t}^{2}\right) \cdot d t$
$v = {\left[5 \cdot t - \frac{2 \cdot {t}^{3}}{3}\right]}_{0}^{5} + C$
$v = \left[5 \cdot 5 - \frac{2 \cdot {5}^{3}}{3}\right] - \left[0\right] + C$
t=0 ;v=30 ;C=30
$v = 25 - \frac{250}{3} + 30$
$v = 55 - \frac{250}{3}$
$v = \frac{165 - 250}{3}$
$V = - 28 , 3 \frac{m}{s}$