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+βt3θ(t)=γt+βt3, where γ=γ= 0.450 rad/srad/s and β=β= 1.10×10−2 rad/s3rad/s3. Part A Calculate the angular velocity of the merry-go-round as a function of time. Express your answer in terms of the variables ββ, γγ, and tt. ωz(t)ωz(t) = nothing rad/srad/s SubmitRequest Answer Part B What is the initial value of the angular velocity? ωzωz = nothing rad/srad/s SubmitRequest Answer Part C Calculate the instantaneous value of the angular velocity ωzωz at t=t= 5.25 ss . ωzωz = nothing rad/srad/s SubmitRequest Answer Part D Calculate the average angular velocity ωav−zωav−z for the time interval t=0t=0 to t=t= 5.25 ss .