Question

What is the average speed of an object that is not moving at `t=0` and accelerates at a rate of `a(t) =t+2` on `t in [3, 5]`?

Answer 1

6`ms^(-1)`

Explanation:

we know that
`a=v/t`
`:. (dv)/(dt)=a`
so `dv=a*dt`
`:. int_0^(v_t)dv=int_3^5(t+2)dt`
`=>[t^2/2+2t]_3^5=12`
this yield us the net sum of velocity at the end from `3^("rd")` to `5^("th")` second. Now we know its been only two second sso upon dividing it with 2 may yield us the average velocity .
`12/2=6 ms^(-1)`