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

Explanation

`a=kt`
Here acceleration is not constant, hence equations of motion are not applicable. Acceleration depends on time.
`a=(dv)/(dt)`

`kt=(dv)/(dt)`
`overset(v=v)underset(v=0)intdv=overset(t=t)underset(t=0)intkt dt {{:("if we are integrating with respect"),("to t, use limits of t in integration"):}}`
`|v|_(0)^(v)=k|t^(2)/2|_(0)^(t)`
`v-0=k(t^(2)/2-0)`
`v=(kt^(2))/2`