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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 v=αX. The displacement of the particle varies with time as

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a

t1/2

b

t3

c

t2

d

t

answer is C.

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Detailed Solution

Given v=αx or (dx/dt)=αxIntegrating, we get∫0x dxx=α∫0t dt∴2x=αtor x=α2t24∝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 v=αX. The displacement of the particle varies with time as