Q) A motorcyclist starts from rest at A and travels in a straight line. For the first part of the motion, the motorcyclist’s displacement x metres from A after t seconds is given by x = 0.6t^2 − 0.004t^3.

(i) Show that the motorcyclist’s acceleration is zero when t = 50 and find the speed V ms^-1 at this time.

For t ≥ 50, the motorcyclist travels at constant speed V ms^-1.

(ii) Find the value of t for which the motorcyclist’s average speed is 27.5ms^-1

My Attempt

I've already done part (i) to get v=30ms^-1

I'm stuck at part (ii). By using calculus or any other easy method kindly show me how to solve this.

Thanks in advance!