Question

A car of mass $m$ starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude $P_0$. The instantaneous velocity of this car is proportional to

• A. $t^{-1/2}$
• B. $t^{1/2}$
• C. $t/\sqrt{m}$
• D. $t^2{P}_0$

Answer 1

The correct option is B $t^{1/2}$

Power delivered can be given as $(F.v)$ where, $F$ is the force applied and $v$ is the velocity of the car.
Or, we can write it as $\left[\right(ma).v]$
Or, $P_0=m\left(\frac{dv}{dt}\right)v$
Or, $vdv=\left(\frac{P_0}{m}\right)dt$
On integrating both sides we get,
$\frac{v^2}{2}=\frac{P_0}{m}t$
Thus, we can say
$v\propto \sqrt{t}$.
Hence, option $\left(C\right)$ is correct.