Question

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

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

Answer 1

The correct option is B 25 kW

Given:
Mass of the body, $m=50kg$
Car starts from rest. So, initial velocity, $u=0{ms}^{-1}$
Final velocity, $v=100{ms}^{-1}$
Time, $t=10s$

The energy provided by the engine is converted to kinetic energy of the car. So, the energy provided by the engine is:
$E=\frac{1}{2}m(v^2-u^2)$
$E=\frac{1}{2}\times 50\times ({100}^2-0^2)$
$E=250000=250kJ$

From definition of power,
$P=\frac{E}{t}$
$P=\frac{250kJ}{10s}=25kW$