Q64 / 120 · NEET 2012 (Mains) · Physics

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
    $t^2 P_0$
  • Correct answer
    B
    $t^{1 / 2}$
  • C
    $t^{-1 / 2}$
  • D
    $t / \sqrt{m}$

Solution

Power $P_0=F v$ $$ \begin{aligned} & =\left(m \frac{d v}{d t}\right) v \\ & =m v \frac{d v}{d t} \end{aligned} $$ Integrating both sides $$ \begin{aligned} \int P_0 d t & =\int m v d v \\ P_0 t & =\frac{m v^2}{2} \\ v^2 & =\frac{2 P_0 t}{m} \\ v & \propto t^{1 / 2} \end{aligned} $$

Hence, the correct answer is option: 'B'.

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