A load is to be raised $23$ ft by the hoisting system shown. Assume that gear $A$ is initially at rest, accelerates uniformly to a speed of $120$ rpm in $5$ s $,$ and then maintains a constant speed of $120$ rpm $.$

Problem $15\mathrm{.}031.$a $-$ Number of revolutions executed by the gear

Determine the number of revolutions executed by gear $A$ in raising the load.

The number of revolutions executed is