The coordinates of a particle moving in x-y plane at any time t are `(2 t, t^2).` Find (a) the trajectory of the particle, (b) velocity of particle at time t and (c) acceleration of particle at any time t.

Answer

A, B, C, D

Explanation

(a) `x=2t rArr t=x/2`
`y=t^2 or y=(x/2)^2`
`:. x^2=4y` is the trajectory
(b) `r=x hati+y hatj=(2thati)+(t^2hatj)`
`v=(dr)/(dt)=(2hati+2t hatj)` units
(c) `a=(dv)/(dt)=(2hatj)` units