A particle located at x=0 at time t...
Question
A particle located at x=0 at time t=0, starts moving along the positive X -direction with a velocity v = α√x. The displacement of the particle varies with time as:
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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=alpha sqrt{x} ). The displacement of the particle varies with time as:
(a) ( t^{3} )
(b) ( t^{2} )
(c) ( t )
(d) ( t^{1 / 2} ).

JEE/Engineering Exams
Physics
Solution
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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 = α√x. The displacement of the particle varies with time as:
Fullscreen

( V=a sqrt{x} )
( frac{d x}{d t}=8 a sqrt{x} )
( frac{d x}{sqrt{x}}=a d t Rightarrow ) in tegreating we ges
( 2 x^{frac{1}{2}}=a+ )
( x=left(frac{a}{2}right)^{2}+2 )

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