Q. 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
Explanation
(c) $\upsilon_{x} = \frac{dx}{dt} = \frac{d}{dt}\left( 3t^{2} - 6t \right) = 6t - 6$. At $t = 1,\ \upsilon_{x} = 0$
$\upsilon_{y} = \frac{dy}{dt} = \frac{d}{dt}\left( t^{2} - 2t \right) = 2t - 2$. At $t = 1,\ \upsilon_{y} = 0$
Hence $\upsilon = \sqrt{\upsilon_{x}^{2} + \upsilon_{y}^{2}} = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.