The position of a particle moving in the xy plane at any time t is given by `x=(3t^2-6t)` metres, `y=(t^2-2t)` metres. Select the correct statement about the moving particle from the following

Options

A. acceleration is zero at t= 0
B. velocity is zero at t= 0
C. velocity is zero at t=1s
D. velocity and acceleration of the particle are never zero.

Answer

C

Explanation

` x = 3 t ^ 2 - 6 t , ` so ( velocity ) `""_x` = ` ( dx ) /( dy ) = 6t - 6 , `
` y = t ^ 2 - 2t `
So, (velocity ) `""_ y ` ` = (dy )/ ( dx ) = 2t - 2 `
At time ` t = 1 `,
` = ( dx ) / (dt ) = 6 xx 1 - 6 = 0 and (dy ) /( dx ) = 2 xx 1 - 2 = 0 `