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

Explanation

`(dx)/(dt)=alphasqrt(x)implies(dx)/(sqrt(x))=alphadt`
on integrating we get `int_(0)^(x)(dx)/(sqrt(x))=int_(0)^(t)alphadt`
[at `t=0,x=0` and let at any time t, particle be at x]
`rArr[(x^(1//2))/(1//2)]_(0)^(x)=alphator x^(1//2)=(alpha)/(2)t=(alpha)/(2)timpliesxalphat^(2)`