Question

What is the average speed of an object that is moving at `12 m/s` at `t=0` and accelerates at a rate of `a(t) =7-t` on `t in [0,4]`?

Answer 1

I found `5m/s`

Explanation:

I do not want to complicate it too much but I would integrate the acceleration to go back to the expression of velocity:
`v(t)=inta(t)dt=int(7-t)dt=7t-t^2/2+c`
now we get the constant `c` by imposing that at `t=0` we have `v(0)=12m/s`. So:
`12=(7*0)-(0)^2/2+c`
so that `c=12m/s`
so the velocity will be:
`v(t)=7t-t^2/2+12`
that at `t=4s` is:
`v(4)=(7*4)-(4^2)/2+12=32m/s`

Average speed will be: `(Deltav)/(Deltat)=(v(4)-v(0))/(4-0)=(32-12)/4=5m/s`