Question

What is the average speed of an object that is moving at `15 m/s` at `t=0` and accelerates at a rate of `a(t) =7-2t^2` on `t in [0,3]`?

Answer 1

`v_a=81/3=27" " m/s`

Explanation:

`v(t)=int(a(t)d t`
`v(t)=int (7-2t^2)d t" "v(t)=7x-2/3t^3+C`
`if t=0" "v=15 m/s" "v(t)=7x-2/3t^3+15`
`Delta x=int_0^3 v(t) d t" "Delta x=int_0^3(7x-2/3t^3+15)d t`
`Delta x=|7/2x^2-2/12t^4+15t|_0^3`
`Delta x=7/2*3^2-2/12*3^4+15*3`
`Delta x=63/2-81/6+45" "Delta x=63/2-27/2+45`
`Delta x=36+45" "Delta x=81`
`v_a=81/3=27" " m/s`