Question

A car is moving on a smooth horizontal road. Find the ratio of work done by the engine of the car, in order to change its speed from $0$ to $v$ and $v$ to $2v$.

• A. $3:1$
• B. $2:3$
• C. $1:3$
• D. $3:2$

Answer 1

The correct option is C $1:3$

Since engine is the source of external force for the car, responsible for its motion,
Applying $W.E.T$,
$W_{\text{engine}}=\Delta K.E\text{of car}$

In first case, speed changes from 0 to $v$
$W_1=\Delta K.E_1$
$=\frac{1}{2}m{v}^2-0=\frac{1}{2}m{v}^2$
In second case, the speed has changed from $v$ to $2v$
i.e $W_2=\Delta K.E_2$
$=\frac{1}{2}m(2v{)}^2-\frac{1}{2}m{v}^2$
$\therefore W_2=\frac{3}{2}m{v}^2$
$\Rightarrow \frac{W_1}{W_2}=\frac{1}{3}$