(A) Given velocity vector: $\vec{v} = v_x \hat{i} + v_y \hat{j} = 3 \hat{i} + 6x \hat{j}$.Comparing components,we get $v_x = \frac{dx}{dt} = 3$ and $v

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(A) Given velocity vector: $\vec{v} = v_x \hat{i} + v_y \hat{j} = 3 \hat{i} + 6x \hat{j}$.Comparing components,we get $v_x = \frac{dx}{dt} = 3$ and $v_y = \frac{dy}{dt} = 6x$.The slope of the path is given by $\frac{dy}{dx} = \frac{v_y}{v_x}$.Substituting the values,$\frac{dy}{dx} = \frac{6x}{3} = 2x$.Integrating both sides with respect to $x$: $\int dy = \int 2x dx$.Since the particle starts from the origin $(0,0)$,the constant of integration is $0$.Thus,$y = x^2$.

Class 11 Physics 3-2.Motion in Plane Motion In Two And Three Dimension

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$A$ particle projected from the origin moves in the $x-y$ plane with a velocity $\vec{v} = 3 \hat{i} + 6x \hat{j}$,where $\hat{i}$ and $\hat{j}$ are the unit vectors along the $x$ and $y$ axes. Find the equation of the path followed by the particle.

A
$y = x^2$
B
$y = \frac{1}{x^2}$
C
$y = 2x^2$
D
$y = \frac{1}{x}$

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3-2.Motion in Plane

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Motion In Two And Three Dimension

$A$ 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?

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$A$ 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:

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

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The coordinates of a moving particle at any time $t$ are given by $x = at^2$ and $y = bt^2$. The speed of the particle at any moment is

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Explain average acceleration and instantaneous acceleration.

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$A$ particle projected from the origin moves in the $x-y$ plane with a velocity $\vec{v} = 3 \hat{i} + 6x \hat{j}$,where $\hat{i}$ and $\hat{j}$ are the unit vectors along the $x$ and $y$ axes. Find the equation of the path followed by the particle.

Similar Questions

$A$ 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?

$A$ 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:

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 coordinates of a moving particle at any time $t$ are given by $x = at^2$ and $y = bt^2$. The speed of the particle at any moment is

Explain average acceleration and instantaneous acceleration.

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