Question

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

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

Answer 1

Answer: (C)

The velocity of the particle is zero at $t = 1$ second

Answer 2

$v_{x} = \frac{dx}{dt} = \frac{d}{dt}(3t^{2} - 6t) = 6t - 6$. At $t = 1,\mspace{6mu} v_{x} = 0$

$v_{y} = \frac{dy}{dt} = \frac{d}{dt}(t^{2} - 2t) = 2t - 2$. At $t = 1,\mspace{6mu} v_{y} = 0$

Hence $v = \sqrt{v_{x}^{2} + v_{y}^{2}} = 0$