A particle starts from rest and moves with acceleration a which varies with time `t` as `a=kt` where `k` is a costant. The displacement `s` of the particle at time `t` is

Options

A. `(1)/(2) k t^(2)`
B. `(1)/(2) a t^(2)`
C. `(1)/(6) a t^(2)`
D. `k t^(3)`

Answer

C

Explanation

`a = kt rArr (dv)/(dt) = kt`
`int dv = int kt dt`
`v = (kt^(2))/(2) rArr (dx)/(dt) = (kt^(2))/(2)`
`int dx = int k (t^(2))/(2) dt`
`x = (kt^(3))/(6) = ((kt)t^(2))/(6) = (1)/(6) a t^(2)`