Aspinning wheel is slowed down by a brake, giving it a constant angular acceleration of −5.40 rad/s2. during a 3.40-s time interval, the wheel rotates through 50.4 rad. what is the angular speed of the wheel at the end of the 3.40-s interval?

The law of motion for the wheel is

where 
is the angle covered after a time interval t
is the initial angular speed of the wheel
is the angular  acceleration of the wheel

We know that after a time t=3.40 s the angle covered by the wheel is 50.4 rad, so we can use these data and re-arrange the previous formula to find the initial angular speed:


And then, the final angular speed will be given by