Answer
a) $t=10s$
b) $\alpha=-2rad/s^2$
Work Step by Step
We have: initial velocity $\omega_0=+20rad/s$, final speed $\omega=0$ and displacement $\theta=+15.92rev\times\Big(\frac{2\pi rad}{1rev}\Big)=100rad$
a) The amount of time it takes for the bike to stop is
$$\theta=\Big(\frac{\omega+\omega_0}{2}\Big)t$$ $$t=\frac{2\theta}{\omega+\omega_0}=10s$$
b) The angular acceleration of each wheel is $$\alpha=\frac{\omega-\omega_0}{t}=-2rad/s^2$$
