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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^(2)`

B

`t`

C

`t½`

D

`t^(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`V = alpha sqrt(x) rArr (dx)/(dt) = alpha. sqrt(x)`
or `(dx)/(sqrt(x)) = alpha. dt`
Perform intengration
`int_(0)^(x) (dX)/(sqrt(x)) = int_(0)^(1) alpha. dt`
[`:'` at `t = 0, x = 0` and let at any time `t`, particle is at `x`]
`rArrr (x^(1//2))/(1//2)|_(0)^(x) = alpha t`
or `x^(1//2) =(alpha)/(2) t`
or `x = (alpha^(2))/(4) xx t^(2)`
or `x prop t^(2)`
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