Aspinning wheel is slowed down by a brake, giving it a constant angular acceleration of 25.60 rad/s2. during a 4.20-s time interval, the wheel rotates through 62.4 rad. what is the angular speed of the wheel at the end of the 4.20-s interval?

We use rotational kinematic equations,

            (A)

                                    (B)                                          

Here, and are final and initial angular displacements respectively,   and are final and initial angular speed and is the angular acceleration.

Given,   and .

Substituting these values in equation (A), we get

Now from equation (B),

Thus, the angular speed of the wheel at the end of the 4.20-s interval is 36.7  rad/s.