Question

A car accelerates from rest to $100m{s}^{-1}$ in ten seconds. If mass of the car is $50kg$, then the average power developed by the engine is:

• A. $25kW$
• B. $30kW$
• C. $35kW$
• D. $40kW$

Answer 1

The correct option is A $25kW$

Given: initial velocity, $u=0$, final velocity, $v=100m{s}^{-1}$, mass, $m=50kg$.
Let the work done by the engine be $w$ and the average power developed be $P$.

Change in kinetic energy $=\frac{1}{2}m{v}^2-\frac{1}{2}m{u}^2$
$=\frac{1}{2}\times m\times v^2$ (as $u=0$)
$=\frac{1}{2}\times 50\times {100}^2=250000J$

As work done equals change in kinetic energy:
$\therefore W=250000J$

Average power, $P=\frac{\text{Total work done}}{\text{total time}}$
$\Rightarrow P=\frac{250000}{10}=25000W=25kW$
Therefore, the average power developed by the engine is $25kW$.