A child is pushing a merry-go-round. The angle through which the merry-go-round has turned varies with time according to θ(t)=γt+βt3, where γ=0.400rad/s and β=0.0120rad/s3.

a) Calculate the angular velocity of the merry-go-round as a function of time.

b) What is the initial value of the angular velocity?

c) Calculate the instantaneous value of the angular velocity ωz at t = 5.00 s and the average angular velocity ωav−z for the time interval t = 0 to t = 5.00 s. Show that ωav−z is not equal to the average of the instantaneous angular velocities at t = 0 and t = 5.00 s, and explain.