The x and y coordinates of a particle at any | vedclass

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

Question

(A) Given the position coordinates of the particle as functions of time $t$:$x = 5t - 2t^2$$y = 10t$To find the velocity components,we differentiate t

Vedclass · Accepted Answer

$-4$

Vedclass · Answer

(A) Given the position coordinates of the particle as functions of time $t$:$x = 5t - 2t^2$$y = 10t$To find the velocity components,we differentiate the position coordinates with respect to time $t$:$v_x = \frac{dx}{dt} = \frac{d}{dt}(5t - 2t^2) = 5 - 4t$$v_y = \frac{dy}{dt} = \frac{d}{dt}(10t) = 10$To find the acceleration components,we differentiate the velocity components with respect to time $t$:$a_x = \frac{dv_x}{dt} = \frac{d}{dt}(5 - 4t) = -4 \, m/s^2$$a_y = \frac{dv_y}{dt} = \frac{d}{dt}(10) = 0 \, m/s^2$The acceleration vector is $\vec{a} = a_x \hat{i} + a_y \hat{j} = -4 \hat{i} + 0 \hat{j} = -4 \hat{i} \, m/s^2$.Since the acceleration components are constant,the acceleration of the particle at any time $t$,including $t = 2 \, s$,is $-4 \, m/s^2$ in the $x$-direction.

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 . . . . . . $m/s^2$.

Similar Questions

$A$ particle moves in space along the path $z = ax^3 + by^2$ in such a way that $\frac{dx}{dt} = c = \frac{dy}{dt}$,where $a, b,$ and $c$ are constants. The acceleration of the particle is:

$A$ particle is moving in the $xy$-plane such that its position coordinates are given by $x = (4t + t^2) \text{ m}$ and $y = (2t + \frac{t^2}{2}) \text{ m}$,where $t$ is in seconds. What is the velocity of the particle?

The position vector of a moving body at any instant of time is given as $\overrightarrow{r} = (5t^2 \hat{i} - 5t \hat{j}) \text{ m}$. The magnitude and direction of velocity at $t = 2 \text{ s}$ is,

The position coordinates of a particle moving in a $3-D$ coordinate system are given by $x = a \cos \omega t$,$y = a \sin \omega t$,and $z = a \omega t$. The speed of the particle is:

Which two motions are considered to be combined for motion in a plane?

Vedclass Test Series

Exam Paper Generator

Online Exam Module