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Q.

A particle located at x=0 at time t=0, starts moving along the positive x-direction with a velocity v that varies as $v = α \sqrt{x}$ . The displacement of the particle varies with time as

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a

t

b

t²

c

$t^{\frac{1}{2}}$

d

t³

answer is B.

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Detailed Solution

$v = α \sqrt{x} or \frac{dx}{dt} = α \sqrt{x} or \int \frac{dx}{\sqrt{x}} = α \int dt or 2 x^{1 / 2} = αt$

or $x = {(\frac{αt}{2})}^{2}$

or displacement is proportional to t²

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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=αx . The displacement of the particle varies with time as