Question

What is the average speed of an object that is still at `t=0` and accelerates at a rate of `a(t) = 16-t^2` from `t in [0, 4]`?

Answer 1

`26 2/3`

Explanation:

given,

`a(t) = 16-t^2`

`=> v(t) = int_o^t(16-t^2)dt = 16t-1/3t^3,` as `v(0) = 0;`

`"avg. speed" = (int_o^4(16t-1/3t^3)dt)/(int_0^4dt) = 1/4(8[t^2]_0^4-1/12 [t^4]_0^4) = (32-16/3) = 26 2/3`