Question

What is the average speed of an object that is still at `t=0` and accelerates at a rate of `a(t) = 5t` from `t in [0,1]`?

Answer 1

The average speed is `=2.5ms^-1`

Explanation:

The acceleration is

`a(t)=5t`

The speed is the integral of the acceleration

`v(t)=inta(t)dt`

Let the average speed be `barv`

Then,

`(1-0)barv=int_0^1 5tdt=[5/2t^2]_0^1`

`barv=5/2=2.5ms^-1`