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

Answer

D

Explanation

From the previous problem solution
`v=(alpha^(2)t)/2`
`(dx)/(dt)=(alpha^(2)t)/2`
`int_(0)^(x)dx=alpha^(2)/2int_(0)^(t)t dt`
`x=alpha^(2)/2.t^(2)/2`
`x alpha t^(2)`