At time t = 0 s, a wheel has an angular displacement of zero radians and an angular velocity of +28 rad/s. The wheel has a constant acceleration of -0.51 rad/s^2. In this situation, the time t, at which the wheel comes to a mandatory halt, is closest to:
The angular displacement of the wheel at time t = 0 is zero radians. The angular velocity of the wheel at time t = 0 is 28 rad/s.
The constant acceleration of the wheel is -0.51 rad/s^2. As the angular acceleration is negative, the angular velocity of the wheel is decreasing.
If the initial angular velocity is u and the final angular velocity after time t is v, the two are related as v = u + a*t where a is the angular acceleration.
Here, u = 28 rad/s, a = -0.51 rad/s^2 and v = 0 rad/s. Substituting these values in the equation provided:
0 = 28 - 0.51*t
=> t = 28/0.51
=> t `~~` 54.90
The wheel comes to a halt in approximately 54.9 seconds.