Question

A car accelerates from rest to 100 $m{s}^{-1}$ in $10seconds$. If the mass of the car is $50kg$ then what will be the power developed by the engine?

• A. 20 kW
• B. 25 kW
• C. 30 kW
• D. 35 kW

Answer 1

The correct option is B 25 kW

Given:
Mass of car $m=50kg$,
Initial velocity of car $u=0m{s}^{-1}$,
Final velocity of car $v=100m{s}^{-1}$,
Time taken $t=10s$
The change in kinetic energy of the car would be equal to the work done by the engine. Since power is work done per unit time, so change in kinetic energy of the car and the time which is taken for the change gives us the power developed by the engine i.e.
Work done $=\frac{1}{2}\times m\times v^2$
Substituting values
$Work=\frac{1}{2}\times 50\times {100}^2=250000J$

Power $=\frac{250000}{10}=25000W=25kW$