A wheel that turns and turns back

A wheel spins at $6.0\ \text{rad/s}$, and a steady torque slows it with $\alpha = -1.2\ \text{rad/s}^2$. It stops for an instant, then turns back. You will make the program follow its angular velocity and angle, and find when it stops and how far it turns before turning back.

The idea. With steady $\alpha$: $\omega = \omega_0 + \alpha t$ and $\theta = \omega_0 t + \tfrac12 \alpha t^2$.

Your tasks.

1. Work out w and theta at every time in t.
2. Find the time at which the wheel stops for an instant.
3. Find the largest angle it reaches before it turns back.