The speed of a motor increases from 1200 rpm to 1800 rpm in 20 sec. How many revolutions does it make in this period of time?

$\begin{array}{r}{\mathrm{\omega }}_1=1200 \mathrm{rpm}=40\mathrm{\pi }{ \mathrm{rad} \mathrm{s}}^{-1}\\ {\mathrm{\omega }}_2=1800 \mathrm{rpm}=60\mathrm{\pi }{ \mathrm{rad} \mathrm{s}}^{-1}\end{array}$
$\begin{array}{l}\mathrm{\alpha }=\frac{{\mathrm{\omega }}_2-{\mathrm{\omega }}_1}{\mathrm{t}}=\frac{60\mathrm{\pi }-40\mathrm{\pi }}{20}=\mathrm{\pi } \mathrm{rad} {\mathrm{s}}^{-2}\\ \mathrm{\theta }={\mathrm{\omega }}_1\mathrm{t}+\frac{1}{2}{\mathrm{\alpha t}}^2\Rightarrow \mathrm{\theta }=1000\mathrm{\pi } \mathrm{rad}\end{array}$
No of revolution $=\frac{\mathrm{\theta }}{2\mathrm{\pi }}=\frac{1000\mathrm{\pi }}{2\mathrm{\pi }}=500$