Achild is pushing a playground 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.

part a calculate the angular velocity of the merry-go-round as a function of time. express your answer in radians per second in terms of γ, β, and t. ω(t) = rad/sec

part part b what is the initial value ω0 of the angular velocity? express your answer in radians per second. ω0 = rad/s

part c calculate the instantaneous value of the angular velocity ω(t) at time t=5.00s. express your answer in radians per second. ω(5.00) = rad/s

part d calculate the average angular velocity ωav for the time interval t=0 to t=5.00 seconds. express your answer in radians per second. ωav = rad/s