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A particle located at x = 0 at time t =...

A particle located at `x = 0` at time `t = 0`, starts moving along with the positive ` x-direction` with a velocity 'v' that varies as ` v = a sqrt(x)`. The displacement of the particle varies with time as

A

` t^(1//2)`

B

` t^(3)`

C

` t^(2) `

D

t

Text Solution

Verified by Experts

The correct Answer is:
C
we are given ` v= alpha sqrt x " "v =(dx)/(dt) alpha sqrt x or (dx)/(sqrt x) =alpha dt `
int _0^(x) (dx)/(sqrtx) =alpha int _0^(t) dt = alpha " "or " " 2x ^(1//2) =alpha t " "or " " x=((alpha )/(2))^(2) t^(2) or " " ` displacement is proportional to `t^(2) `
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