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

A.

B. 0.4 rad/s

C. 1.3 rad/s

D. 0.7 rad/s

Explanation:

Part A. We can take the derivative of the motion function in order to get the angular velocity function with respect to time

Part B. The initial value of angular velocity is when t = 0

Part C. The instantaneous value of the angular velocity at t = 5s

Part D. The angle distance it travels during the first t = 5 seconds is

So the average angular velocity during this 5 seconds would be the total angle traveled divided by the time

are their multiple choices ?

explanation:

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.