Answer
The angular displacement of the wheel from $t=0$ to $t=8s$ is $24rad$
Work Step by Step
We examine the change in angular velocity from $t=3$ to $t=5s$ to find angular acceleration $\alpha$
We have $\omega_0=0rad/s$, $\omega=+6rad/s$ and $t=2s$
$$\alpha=\frac{\omega-\omega_0}{t}=3rad/s^2$$
From $t=0$ to $t=8s$, we have $\omega_0=-9rad/s$, $\Delta t=8s$
The angular displacement of the wheel from $t=0$ to $t=8s$, therefore, is $$\theta=\omega_0t+\frac{1}{2}\alpha t^2=24rad$$
