The coordinates of a moving particle at any t | vedclass

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

Question

(C) Given the position coordinates of the particle as $x = \alpha t^3$ and $y = \beta t^3$.The velocity components are obtained by differentiating the

Vedclass · Accepted Answer

$3t^2\sqrt{\alpha^2 + \beta^2}$

Vedclass · Answer

(C) Given the position coordinates of the particle as $x = \alpha t^3$ and $y = \beta t^3$.The velocity components are obtained by differentiating the position with respect to time $t$:$v_x = \frac{dx}{dt} = \frac{d}{dt}(\alpha t^3) = 3\alpha t^2$$v_y = \frac{dy}{dt} = \frac{d}{dt}(\beta t^3) = 3\beta t^2$The speed $v$ of the particle is the magnitude of the velocity vector:$v = \sqrt{v_x^2 + v_y^2}$$v = \sqrt{(3\alpha t^2)^2 + (3\beta t^2)^2}$$v = \sqrt{9\alpha^2 t^4 + 9\beta^2 t^4}$$v = \sqrt{9t^4(\alpha^2 + \beta^2)}$$v = 3t^2\sqrt{\alpha^2 + \beta^2}$

The coordinates of a moving particle at any time $t$ are given by $x = \alpha t^3$ and $y = \beta t^3$. The speed of the particle at time $t$ is given by

Similar Questions

The position vector of an object at any time $t$ is given by $\vec{r} = 3t^2 \hat{i} + 6t \hat{j} + \hat{k}$. Its velocity along the $y$-axis has the magnitude:

Explain the position and displacement vectors for a particle moving in a plane using suitable equations.

The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 7t + 4t^2$ and $y = 5t$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The acceleration of the particle at $t = 5 \ s$ is ......... $m/s^2$.

The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 5t - 2t^2$ and $y = 10t$ respectively,where $x$ and $y$ are in meters and $t$ is in seconds. The acceleration of the particle at $t = 2 \, s$ is . . . . . . $m/s^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module