The distance x covered by a paritcle in one dimensional motion varies with time t as x ^ 2 = a t ^ 2 + 2bt + c . If the acceleration of the particle depends on x as x ^ - n , where n is an integer, the value of n is

Correct answer: 0 x ^ 2 = a t ^ 2 + 2bt + c 2xv = 2at + 2b xv = at + b v ^ 2 + ax = a ax = a - ((at + b)/(x)) ^ 2 a = a(a t ^ 2 + 2bt + c) - (at + b) ^ 2 x ^ 3 a = a c ^ - 2 x ^ 3 aα x ^ - 3

JEE Main 20209 JanuaryMorning Shift

Exam: JEE Main
Year: 2020
Date: 9 January
Shift: Morning Shift
Subject: Physics
Chapter: Motion in One Dimension

JEE Main 2020 · 9 January · Morning Shift · Physics · Motion in One Dimension

The distance x covered by a paritcle in one dimensional motion...

The distance

x

covered by a paritcle in one dimensional motion varies with time

t

{x}^{2} = a{t}^{2} + 2bt + c

. If the acceleration of the particle depends on

x

{x}^{- n}

, where

n

is an integer, the value of

n

is _________

Correct answer

Step-by-step solution

{x}^{2} = a{t}^{2} + 2bt + c

2xv = 2at + 2b

xv = at + b

{v}^{2} + ax = a

ax = a - {\left(\dfrac{at + b}{x}\right)}^{2}

a = \dfrac{a\left(a{t}^{2} + 2bt + c\right) - {\left(at + b\right)}^{2}}{{x}^{3}}

a = \dfrac{a{c}^{- 2}}{{x}^{3}}

a\alpha{x}^{- 3}

Practice Motion in One Dimension on Quantrex Academy →

More from Motion in One Dimension

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a… JEE Main 2026 Two masses of 3.4 kg and 2.5 kg are accelerated from an initial speed of 5 m/s and 12… JEE Main 2026 The velocity ( v ) versus time ( t ) plot of a particle is shown in the figure, for a… JEE Main 2026 From 18 m height above the ground a ball is dropped from rest. The height above the… JEE Main 2026 Two cars A and B are moving in the same direction along a straight line with speeds 100… JEE Main 2026 The velocity of a particle is given as v = -x i + 2y j - z k m/s. The magnitude of… JEE Main 2026 A particle starts moving from time t=0 and its coordinate is given as x(t)=4 t^ 3 -3 t A.… JEE Main 2026 Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the… JEE Main 2026 Full Motion in One Dimension list All JEE Main PYQs