A child is pushing a merry$-$go$-$round. The angle through which the merry$-$go$-$round has turned varies with time according to $0($t$)=$ yt $+$ Bt$\text{'},$ wherey $=0\mathrm{.}400$ rad$/$s and B $=0\mathrm{.}0120$ rad$/$s$*.($a$)$ Calculate the angular velocity of the merry$-$go$-$round as a function of time. $($b$)$ What is the initial value of the angular velocity? $($c$)$Calculate the instantaneous value of the angular velocity we at t $=5\mathrm{.}00$ s and theaverage angular velocity wav$-$z for the time interval t $=0$ to t $=5\mathrm{.}00$ s$.$ Show that Wav$-$z isnot equal to the average of the instantaneous angulr velocities at t $=0$ and t $=5\mathrm{.}00$ s$,$ and explain.