1. The problem statement, all variables and given/known data 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= 0.383 rad/s and β= 1.00×10−2rad/s3. Calculate the average angular velocity ωav−z for the time interval t=0 to t= 5.50s. 2. Relevant equations Given 3. The attempt at a solution Okay so I solved all the questions above this one which gave me the final and initial angular velocities and I got ωi = 0.383 rad/s and ωf = 1.29 rad/s. When I calculate average angular velocity, why can't I use (ωi + ωf)/2 Instead, I have to use (Θf - Θi)/5.50 to get the correct answer. Shouldn't the first equation yield the same result because an average is the sum of the velocities divided by 2?