Question

What is the average speed of an object that is moving at `2 m/s` at `t=0` and accelerates at a rate of `a(t) =t+1` on `t in [1,2]`?

Answer 1

`v=5/2+2=9/2 m/s`

Explanation:

`v=int _1^2 a(t)*d t`
`v=int _1^2 (t+1)d t`
`v=[1/2 t^2+t]_1^2+C`
`v=[2+2]-[1/2+1]+C`
`v=4-3/2+C`
`v=5/2+C`
`"if t=0 ; v=2; C=2"`
`v=5/2+2=9/2 m/s`