The position of a particle moving in the xy- | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given position coordinates are $x = 3t^2 - 6t$ and $y = t^2 - 2t$.The velocity components are obtained by differentiating position with respect to

Vedclass · Accepted Answer

The velocity of the particle is zero at $t = 1 \, s$.

Vedclass · Answer

(C) Given position coordinates are $x = 3t^2 - 6t$ and $y = t^2 - 2t$.The velocity components are obtained by differentiating position with respect to time $t$:$v_x = \frac{dx}{dt} = 6t - 6$$v_y = \frac{dy}{dt} = 2t - 2$The velocity vector is $\vec{v} = v_x \hat{i} + v_y \hat{j}$.At $t = 1 \, s$:$v_x = 6(1) - 6 = 0 \, m/s$$v_y = 2(1) - 2 = 0 \, m/s$Thus,the velocity $\vec{v} = 0 \hat{i} + 0 \hat{j} = 0$ at $t = 1 \, s$.The acceleration components are obtained by differentiating velocity with respect to time $t$:$a_x = \frac{dv_x}{dt} = 6 \, m/s^2$$a_y = \frac{dv_y}{dt} = 2 \, m/s^2$Since the acceleration is constant and non-zero,it is never zero.Therefore,the correct statement is that the velocity of the particle is zero at $t = 1 \, s$.

The position of a particle moving in the $xy-$ plane at any time $t$ is given by $x = (3t^2 - 6t) \, m$ and $y = (t^2 - 2t) \, m$. Select the correct statement about the moving particle from the following:

Similar Questions

$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is:

The first step of taxonomy is .......... .

The protective coat of structural protein in viruses is made up of units called:

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then,the probability for the ball chosen to be white is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module