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

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!

(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!

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