Halliday, Resnick & Walker — Rotation: Problem 8

8 The angular acceleration of a wheel is $\alpha = 6.0t^4 - 4.0t^2$, with $\alpha$ in radians per second-squared and $t$ in seconds. At time $t = 0$, the wheel has an angular velocity of $+2.5 \text{ rad/s}$ and an angular position of $+1.5 \text{ rad}$. Write expressions for (a) the angular velocity (rad/s) and (b) the angular position (rad) as functions of time (s).