Question

The position of a particle moving in the xy-plane at any time 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

The correct option is C The velocity of the particle is zero at t = 1 second

$v_x=\frac{dx}{dt}=\frac{d}{dt}(3t^2-6t)=6t-6.$ At $t=1,v_x=0$
$v_y=\frac{dy}{dt}=\frac{d}{dt}(t^2-2t)=2t-2.$ At $t=1,v_y=0$
Hence $v=\sqrt{v_x^2+v_y^2}=0$