The angular speed of the wheel of a vehicle is increased from,...

Given, $t = 14s$, ${\omega}_{0} = \dfrac{360}{60}rps = 12\pi rad{s}^{- 1}$, and $\omega = \dfrac{1200}{60}rps = 40\pi rad{s}^{- 1}$. Now use the first equation of motion in rotation motion, in terms of angular acceleration and angular velocities,

$\omega = {\omega}_{0} + \alphat$$⇒ \alpha = \dfrac{\omega - {\omega}_{0}}{t} = \dfrac{28\pi}{14} = 2\pi rad{s}^{- 2}$.