# What is the average speed of an object that is still at t=0 and accelerates at a rate of a(t) =t^2-4 from t in [2, 3]?

Jan 12, 2018

4.58 $\frac{m}{\sec}$

#### Explanation:

Acceleration of the object is given as,$a = 4 {t}^{2} - 4$
So,velocity will be $\frac{{t}^{3}}{3} - 4 t$ (by integrating)
Hence,displacement will be,
$S = \frac{{t}^{4}}{12} - \left(2 {t}^{2}\right)$ (by integrating)
Hence,displacement with in t=2 to t=3 will be -4.58 meter
Now here distance=displacement that has happened in between 2 sec and 3 sec
Hence average speed with in this duration=(total distance covered/total time)
I.e $\left(\frac{4.58}{1}\right)$ $\frac{m}{\sec}$ or 4.58 $\frac{m}{\sec}$