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A variable counterclockwise torque is first applied to a flywheel at time $t=0.$ The flywheel originally rotates freely at $1500re\frac{v}{m}in$ clockwise. The torque produces counterclockwise angular acceleration $=5$tra$\frac{d}{s^2},$ where $t$ is the time in seconds. Determine:

$($a$)$ the time required for the flywheel to reduce its clockwise angular speed to $700$ rev$/$min$,$

$($b$)$ the time required for the flywheel to reverse its direction of rotation, and

$($c$)$ the total number of revolutions, the first $10$ seconds of torque application.

C

Answer: $146\mathrm{.}8$ rad