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+βt^{3}, where γ=0.422 rad/s and β=1.45∗10^{−2} rad/s^{3}.

Part A: Calculate the angular velocity of the merry-go-round as a function of time. Express your answer in terms of the variables β,γβ,γ and t.

Part B: What is the initial value of the angular velocity?

Part C: Calculate the instantaneous value of the angular velocity ωzωz at t = 4.60 s.

Part D: Calculate the average angular velocity for the time interval t=0 to t= 4.60 s.