Answer
$4.8\ s$
Work Step by Step
The angular speed is given by $ω_o=10 rev/s$
Angular position $Δθ=60\ rev$
The final angular speed is $ω=15\ rev/s$
From rotational kinematics equations, we have the formula :
$\Delta\theta=\frac{1}{2}(\omega_o+\omega)\Delta t$
$\Delta t=\frac{2\Delta\theta}{\omega_o+\omega}$
$\Delta t=\frac{2(60\ rev)}{10\ rev/s +15\ rev/s}$
$\Delta t =4.8\ s$
