The position of a particle moving in the x-y plane at any time t is given by: x = (3t³ - 6t) meters; y = (t² - 2t) meters. Select the correct statement.

Given : x = (3t³ - 6t) meters and y = (t² - 2t) meters
For x direction : vx = dx/dt = 9t² - 6; ax = d²x/dt² = 18t
For y direction : vy = dy/dt = 2t - 2; ay = d²x/dt² = 2
Hence at t=0, ax = 0 But ay = 2 = constant, thus acceleration can never become zero
Also, vy = 0 at t = 1s but vx ≠ 0 at t = 1s
And at t = √(2/3)s, vx = 0 but vy ≠ 0
Thus vx and vy can never become zero at the same instant. So, velocity and acceleration can never become zero.