Awind turbine is initially spinning at a constant angular speed. as the wind's strength gradually increases, the turbine experiences a constant angular acceleration 0.101 rad/s2. after making 2870 revolutions, its angular speed is 149 rad/s. (a) what is the initial angular velocity of the turbine? (b) how much time elapses while the turbine is speeding up?

Let us list the given: 

constant acceleration = 0.101 rad/s^2
angular distance = 2870 revolutions 
*since 1 revolution = 2π rad, this is equal to 5740π rad (2870*2π)
angular speed = 149 rad/s

From here, we could infer that it is easier to determine letter b first. To solve for time, just divide distance by speed

b.) time = 5740π/149 rad/s = 121.03 seconds

a.) For letter a, we use the formula for acceleration

a = (v,final - v,initial)/t
0.101 rad/s^2= (149 rad/s - v,initial)/121.03 s
v,initial = 136.78 rad/s