Question

The position of a particle moving in the X-Y plane from origin at any time $t$ is given by $x=(3t^2-6t)$ m; $y=(t^2-2t)$ m, where $t$ is in seconds. Select the correct statement(s) 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

$\hat{i}\to x$
$\hat{j}\to y$

$a=\frac{d^{2}x}{d{t}^2}\hat{i}+\frac{d^{2}y}{d{t}^2}\hat{j}$

$a=6\hat{i}+2\hat{j}$

$v=\frac{dx}{dt}\hat{i}+\frac{dy}{dt}\hat{j}=(6t-6)\hat{i}+(2t-2)\hat{j}$

$v(t=0)=-6\hat{i}-2\hat{j}$
$v(t=1)=0\hat{i}+0\hat{j}=0$