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Question

A particle located at x=0 at time t=0, starts moving along the positive xdirection with a velocity v that varies as v=αx. The displacement of the particle varies with time as

A
t2
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B
t
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C
t1/2
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D
t3
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Solution

The correct option is A t2
Given, v=αx
As we know that, v=dxdt, where, x is the displacement of the particle.
dxdt=αx
x0dxx=t0α dt
[x1/21/2]x0=αt
x=αt2
x=α2t24
xt2
Hence, displacement will varies with time as xt2

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