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JEE Main 20246 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 6 April
Shift: Evening Shift
Subject: Physics
Chapter: Motion in One Dimension

JEE Main 2024 · 6 April · Evening Shift · Physics · Motion in One Dimension

A particle moves in a straight line so that its displacement x at...

A particle moves in a straight line so that its displacement

x

at any time

t

is given by

x^2=1+t^2

. Its acceleration at any time

\mathrm{t}

is

x^{-\mathrm{n}}

where

\mathrm{n}=

___________

Correct answer

0

Step-by-step solution

\begin{aligned} & \mathrm{x}^2=1+\mathrm{t}^2 \\ & 2 \mathrm{x} \frac{\mathrm{dx}}{\mathrm{dt}}=2 \mathrm{t} \\ & \mathrm{xv}=\mathrm{t} \\ & \mathrm{x} \frac{\mathrm{dv}}{\mathrm{dt}}+\mathrm{v} \frac{\mathrm{dx}}{\mathrm{dt}}=1 \\ & \mathrm{x} \cdot \mathrm{a}+\mathrm{v}^2=1 \\ & \mathrm{a}=\frac{1-\mathrm{v}^2}{\mathrm{x}}=\frac{1-\mathrm{t}^2 / \mathrm{x}^2}{\mathrm{x}} \\ & \mathrm{a}=\frac{1}{\mathrm{x}^3}=\mathrm{x}^{-3}\end{aligned}

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