Question

A car of mass $m$ starts from rest at time $t=0$ and is driven on a straight horizontal road by the engine which exerts a constant force $F$. If friction is negligible, the car acquires kinetic energy $E$ at time $t$ and develops a power $P$.
Which of the following is/are correct?

• A. $E\propto t$
• B. $E\propto t^2$
• C. $P\propto t^{1/2}$
• D. $P\propto t^2$

Answer 1

The correct option is B $E\propto t^2$

Since $F$ is constant, acceleration $a=\frac{F}{m}$ is constant.
At time $t$, the velocity of the car is
$v=u+at=0+at=at=\frac{Ft}{m}$

$\therefore$ Kinetic energy $E$ at time $t$
$E=\frac{1}{2}m{v}^2=\frac{1}{2}m{\left(\frac{Ft}{m}\right)}^2=\left(\frac{F^2}{2m}\right)t^2$
Since $F$ is constant, $E\propto t^2$.

Power $P$ at time $t$ is $P=Fv=F\times \frac{Ft}{m}=\left(\frac{F^2}{m}\right)t$
Thus $P\propto t$.

So the correct option is (b)