A child is pushing a playground merry$-$go$-$round. The angle through which the merry$-$go$-$round has turned varies with time according to $($t$)=$t$+$t$3$$($t$)=$t$+$t$3,$ where $=0\mathrm{.}400$rad$/$s$=0\mathrm{.}400$rad$/$s and $=0\mathrm{.}0120$rad$/$s$3$$=0\mathrm{.}0120$rad$/$s$3.$

Calculate the angular velocity of the merry$-$go$-$round as a function of time.

Express your answer in radians per second in terms of $,$ $,$ and tt$.$

What is the initial value $0$$0$ of the angular velocity?

Express your answer in radians per second.

View Available Hint$($s$)$for Part B

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

$0$$0=$

nothing

rad$/$srad$/$s

Submit

Part C

Calculate the instantaneous value of the angular velocity $($t$)$$($t$)$ at time t$=5\mathrm{.}00$st$=5\mathrm{.}00$s$.$

Express your answer in radians per second.

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$(5\mathrm{.}00)$$(5\mathrm{.}00)=$

nothing

rad$/$srad$/$s

SubmitRequest$$Answer

Part D

Calculate the average angular velocity avav for the time interval t$=0$t$=0$ to t$=5\mathrm{.}00$t$=5\mathrm{.}00$ seconds.

Express your answer in radians per second.