The angular speed of the wheel of a vehicle is increased from, 360 rpm to 1200 rpm in 14 s . Its angular…

Given, $t=14 \mathrm{s}$, ${\omega }_0=\frac{360}{60} \mathrm{rps}=12\pi \mathrm{rad} {\mathrm{s}}^{-1}$, and $\omega =\frac{1200}{60} \mathrm{rps}=40\pi \mathrm{rad} {\mathrm{s}}^{-1}$. Now use the first equation of motion in rotation motion, in terms of angular acceleration and angular velocities, 

$\omega ={\omega }_0+\alpha t$$\Rightarrow \alpha =\frac{\omega -{\omega }_0}{\mathrm{t}}=\frac{28\pi }{14}=2\pi \mathrm{rad} {\mathrm{s}}^{-2}$.