Answer
a) $\alpha=-22.06rad/s^2$
b) $t=0.68s$
Work Step by Step
The skater has initial velocity $\omega_0=+15rad/s$, final velocity $\omega=0$ and displacement $\theta=+5.1rad$
a) Her average angular acceleration is $$\omega^2=\omega_0^2+2\alpha\theta$$ $$\alpha=\frac{\omega^2-\omega_0^2}{2\theta}=-22.06rad/s^2$$
b) The time during which she comes to rest is $$t=\frac{\omega-\omega_0}{\alpha}=0.68s$$
