Rotational Kinematics Practice Test

A ceiling fan blade rotating at $$10 , \text{rad/s}$$ is switched off and slows down with a constant angular acceleration of magnitude $$2.0 , \text{rad/s}^2$$. Through what angle does the blade rotate before coming to rest?

The angular position of a spinning wheel is given by $$\theta(t) = \frac{1}{3}t^3 - \frac{5}{2}t^2 + 6t$$, where $$t$$ is in seconds and $$\theta$$ is in radians. For $$t>0$$, at what time does the wheel first momentarily reverse its direction of rotation?