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Q.

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

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a

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

b

$t^{- \frac{1}{2}}$

c

$\frac{t}{\sqrt{m}}$

d

$t^{2}$

answer is B.

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Detailed Solution

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Power $p_{0} = Fv = (m \frac{dv}{dt}) v = mv \frac{dv}{dt}$

Integrating both sides

$\int p_{0} dt = \int mv dv \Rightarrow p_{0} t = \frac{{mv}^{2}}{2}$

$v^{2} = \frac{2 p_{0} t}{m} \Rightarrow v \propto t^{\frac{1}{2}}$

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A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0. The instantaneous velocity of this car is proportional to