Answer
$3.37s$
Work Step by Step
1) Find the angular acceleration
We have $\omega_0=1.05\times10^4rad/s$, $\omega=3.14\times10^4rad/s$ and $\theta=1.88\times10^4rad$
$$\alpha=\frac{\omega^2-\omega_0^2}{2\theta}=2.33\times10^4rad/s^2$$
2) In the 2nd situation, we have $\omega_0=0$, $\omega=7.85\times10^4rad/s$ and $\alpha=2.33\times10^4rad/s^2$
The time it takes the bit to reach its maximum speed is $$t=\frac{\omega-\omega_0}{\alpha}=3.37s$$
