A particle located at \( x=0 \) at time \( t=0 \), starts moving al...

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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
\( \mathrm{P} \) \( v=\alpha \sqrt{x} \). The displacement of the particle varies with time

W as
[AIEEE 2006]
(a) \( t \)
(b) \( t^{1 / 2} \)
(c) \( \mathrm{t}^{3} \)
(d) \( \mathrm{t}^{2} \)
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