A car of mass ' $m$ ' moving with velocity ' $u$ ' on a straight road in a straight line, doubles its…
A car of mass ' $m$ ' moving with velocity ' $u$ ' on a straight road in a straight line, doubles its velocity in time $t$. the power delivered by the engine of a car for doubling the velocity is
$\frac{3 \mathrm{mu}^2}{2 \mathrm{t}}$
$\frac{\mathrm{mu}^2}{2 \mathrm{t}}$
$\frac{2 \mathrm{mu}^2}{\mathrm{t}}$
$\frac{3 \mathrm{mu}^2}{\mathrm{t}}$
Solution
Initial kinetic energy $\mathrm{k}_1=\frac{1}{2} \mathrm{mu}^2$
Final kinetic energy $\mathrm{k}_2=\frac{1}{2} \mathrm{mu}_2^2=\frac{1}{2} \mathrm{~m}(2 \mathrm{u})^2=\frac{1}{2}\left(4 \mathrm{mu}^2\right)$
$\therefore \mathrm{k}_2-\mathrm{k}_1=\frac{3}{2} \mathrm{mu}^2$
Change in K.E. is work done
Power, $\mathrm{P}=\frac{\text { workdone }}{\mathrm{t}}=\frac{3 \mathrm{mu}^2}{2 \mathrm{t}}$