Question

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]`?

Answer 1

4.58 `m/sec`

Explanation:

Acceleration of the object is given as,`a=4t^2-4`
So,velocity will be `(t^3)/3-4t` (by integrating)
Hence,displacement will be,
`S=(t^4)/12-(2t^2)` (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 `(4.58/1)` `m/sec` or 4.58 `m/sec`