Answer
The amount of time it takes to reach operating speed is $1.3s$
Work Step by Step
The dryer's initial speed is $\omega_0=0$ and the operating speed is $\omega=5.2rad/s$. It has an average acceleration of $\overline\alpha=4rad/s^2$
The amount of time it takes to reach the operating speed is $$\Delta t=\frac{\omega-\omega_0}{\overline\alpha}=1.3s$$
