A heavy flywheel is accelerated (rotationally) by a motor that provides constant torque and therefore a constant angular acceleration alpha. The flywheel is assumed to be stationary at time t = 0 in Parts A, B, and C of this problem.

a). Find the time t_10 it takes to accelerate the flywheel to 10.0 rps (revolutions per second) if alpha is 5.00 radians/s^2.

b). Find the time t to accelerate the flywheel from rest up to angular velocity omega_1.

Express your answer in terms of alpha and omega_1.

c). Find the angle theta_1 through which the flywheel will have turned during the time it takes for it to accelerate from rest up to angular velocity omega_1.

Express your answer in terms of any of the following: omega_1, alpha, and/or t_1.

d). Assume that the motor has accelerated the wheel up to an angular velocity omega_1 with angular acceleration alpha in time t_1. At this point, the motor is turned off, and a brake is applied that decelerates the wheel with a constant angular acceleration of -5alpha. Find t_2, the time it will take the wheel to stop after the brake is applied (that is, the time for the wheel to reach zero angular velocity).

Express your answer in terms of any of the following: omega_1, alpha, and/or t_1.