A particle located at x = 0 at time t=0 starts moving along positive x-direction with velocity v that varies as `v = asqrt(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

Here `v=ax^(1//2)`
`(dx)/(dt)=ax^(1//2)`
or `x^(-1//2)dx=a dt`
Intergrating, we get
`(x^(1//2))/(1//2)`=at `xprop t^(2)`