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JEE Main 2006

Exam: JEE Main
Year: 2006
Subject: Physics
Chapter: Motion in One Dimension

JEE Main 2006 · Physics · Motion in One Dimension

A particle located at x=0 at time t=0 , starts moving along the...

A particle located at

x=0

at time

t=0

, starts moving along the positive

x

-direction with a velocity '

v

' that varies as

v=\alpha \sqrt{x}

. The displacement of the particle varies with time as

Options

A $t^3$
B $t^2$
C $t$
D $t^{1 / 2}$

Correct answer

B. $t^2$

Step-by-step solution

\frac{\mathrm{d} x}{\mathrm{dt}}=\alpha \int \frac{\mathrm{dx}}{\sqrt{\mathrm{x}}}=\int \alpha \mathrm{dt} \Rightarrow \mathrm{x} \alpha \mathrm{t}^2

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