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 A $t^{1/2}$

Power =F.V

Power delivered as at

Cont. magnitude $P_0$

$P_0=F.V$

$P_0=ma\times V$

$\frac{P_0}{m}=\frac{dv}{dt}\times V$

$\left(\frac{P_0}{m}\right){\int }_0^{t}dt={\int }_0^{v}vdv$

$\frac{P_{0}t}{m}=\frac{V^2}{2}$

$V^2=\left(\frac{2P_0}{m}\right)t$

$V=\sqrt{\frac{2P_0}{m}}\times t^{\frac{1}{2}}$

$V\alpha t^{\frac{1}{2}}$