The pulley at point $\backslash ($ A $\backslash )$ is driven by an electric motor. It is connected by a belt to pulley C $,$ where it is used to lift or lower cylinder B $.$ Find the distance that block $\backslash ($ B $\backslash )$ rises in response to the following operating characteristics:

The initial speed of the motor is zero RPM$.$ The operating speed of the motor is $600$ rotations per minute. The motor requires $0\mathrm{.}75$ seconds to go from stopped to its operating speed. The startup of the motor may be assumed to have constant acceleration. After the start time has elapsed, the motor operates at a constant speed.

In this scenario, the motor operates for three seconds after the operating speed is reached. After this, it comes to a stop instantly at a time of $3\mathrm{.}75$ seconds after rotation begins.