Verified Solution • 2025–26 Session moderate

QJEEM21Phfe88: JEE Main 2021 Physics - Class 11 JEEM21Phfe88 Solution: An automobile of mass 'm' accelerates starting from origin and…

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

Multiple Choice Options

A (9P8m)12t32
B (8P9m)12t23
C (9m8P)12t32
D (8P9m)12t32

Step-by-Step Verified Solution

P = const.

P = F v = \frac{m v^{2} d v}{d x}

\int_{0}^{x} \frac{P}{m} d x = \int_{0}^{v} v^{2} d v

\frac{P x}{m} = \frac{v^{3}}{3}

{(\frac{3 P x}{m})}^{1 / 3} = v = \frac{d x}{d t}

{(\frac{3 P}{m})}^{1 / 3} \int_{0}^{t} d t = \int_{0}^{x} x^{- 1 / 3} d x

\Rightarrow x = {(\frac{8 P}{9 m})}^{1 / 2} t^{3 / 2}

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