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NEET 2012
Exam
NEET
Year
2012
Subject
Physics
Chapter
Work, Power and Energy

NEET 2012 · Physics · Work, Power and Energy

A car of mass m starts from rest and accelerates so that the...

A car of mass mm starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P0P_0. The instantaneous velocity of this car is proportional to

Options

  1. At2P0t^2 P_0
  2. Bt1/2t^{1 / 2}
  3. Ct−1/2t^{-1 / 2}
  4. Dt/mt / \sqrt{m}

Correct answer

B. t1/2t^{1 / 2}

Step-by-step solution

Power P0=FvP_0=F v=(mdvdt)v=mvdvdt\begin{aligned}& =\left(m \frac{d v}{d t}\right)v \\ & =m v \frac{d v}{d t} \end{aligned}IntegratingbothsidesIntegrating both sides\begin{aligned}\intP_0 d t & =\intm v d v \\ P_0 t & =\frac{m v^2}{2}\\ v² & =\frac{2 P_0 t}{m}\\ v & \propto t^{1 / 2} \end{aligned}$$
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