Work Energy And Power Question 257
Question: A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude pg. The instantaneous velocity of this car is proportiourl to:
Options:
A) $ {t^{2}}p _{o} $
B) $ {t^{1/2}} $
C) $ {t^{-1/2}} $
D) $ \frac{t}{\sqrt{m}} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Constant power of car $ P_0=F.V=ma.v $
$ P_0=m\frac{dv}{dt}.v $
$ P_0dt=mvdv $ Integrating $ P_0.t=\frac{mv^{2}}{2}v=\sqrt{\frac{2P_0t}{m}} $
$ \because ~~P_0, $ m and 2 are constant
$ \therefore v\propto \sqrt{t} $
