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

Options

A. `t^(2)`
B. t
C. `t^(1//2)`
D. `t^(3)`

Answer

A

Explanation

`v= alpha sqrtx, (dx)/(dt) = alpha sqrtx rArr (dx)/(sqrtx) = alpha dt`
`underset(0)overset(x)int (dx)/(sqrtx) = alpha underset(0)overset(t)int dt [(2 sqrtx)/(1)]_(0)^(x) = alpha [t]_(0)^(t) rArr 2 sqrtx = alpha t rArr x = (alpha^(2))/(4) t^(2)`