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= 0.400 rad/s and β= 0.0145 rad/s3. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Calculating angular velocity.

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