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

Answer

C

Explanation

`v = alpha sqrtx`
`(dx)/(dt) = alpha x^(1//2)`
`underset(0)overset(t)int (dx)/(x^(1//2)) = alpha underset(0)overset(t)int dt`
`(x^(1//2))/(1//2) = alpha t`
`x = (alpha^(2) t^(2))/(4)`
`x prop t^(2)`