Given $s(t) = -t^3 + 2t^2 + \frac32$ be the position of particle moving along $x$ axis at time $t$. At what time will the instantaneous velocity equal the average velocity over the time interval [0,4]?
Instantaneous velocity = $\frac{ds}{dt}= -3t^2 + 4t$
Average velocity = $\frac{s(t)-s(0)}{t} = -t^2 + 2t$
So I need to solve $-3t^2 + 4t = -t^2 + 2t $ for $t$ right?
Is this correct?