A particle is moving under constant acceleration `a=k t`. The motion starts from rest. The velocity and displacement as a function of time t is

Options

A. `kt^(2),kt^(3)`
B. `(kt^(2))/(2),(kt^(3))/(3)`
C. `(kt^(3))/(2),(kt^(2))/(3)`
D. `(kt^(2))/(2),(kt^(3))/(6)`

Answer

D

Explanation

`(dv)/(dt) = a =kt implies int _(0) ^(v) dv =int_(0) ^(t)kt dt`
`v=(1)/(2)kt^(2), (ds)/(dt)=v=(1)/(2) kt^(2)`
`int ds =(k)/(2)int _(0)^(t) t^(2)dt implies s =(kt^(3))/(6)`