Answer
$\theta=75rad$
Work Step by Step
We can use the kinematic equation, $\theta=\omega_0 t +\frac{1}{2}\alpha t^2$, to determine the total additional angle that the disc will turn in the next 5s.
The initial angular velocity for the next 5s is $10rad/s$ (part c).
The initial angular acceleration is $2.0rad/s^2$ (part a).
Therefore;
$\theta=\omega_0 t +\frac{1}{2}\alpha t^2$ $=(10rad/s)(5.0s)+\frac{1}{2}(2.0rad/s^2)(5.0s)^2=75rad$
