Starting from rest at t = 0 s, a wheel undergoes a constant angular acceleration. when t = 3.8 s, the angular velocity of the wheel is 4.8 rad/s. the acceleration continues until t = 20 s, when the acceleration abruptly changes to 0 rad/s2. through what angle does the wheel rotate in the interval t = 0 s to t = 55 s?

Total displacement will be 1136.79 rad

Explanation:

We have given that wheel starts from the rest so initial angular velocity

Angular velocity after 3.8 sec is given as 4.8 rad/sec

So

From second equation of motion we know that

This acceleration is constant until 20 sec

So displacement in 20 sec

Total time is given as t = 55 sec

So left time = 55 - 20 =35 sec

After 20 sec angular acceleration is 0

So displacement in 35 sec

Angular velocity after 20 sec

So displacement  

So total displacement in 55 sec = 252.62 +884.17 = 1136.79 rad