(D) The position vector of the ant is given by $\vec{S} = 2t^2 \hat{j} + 5 \hat{k}$.Velocity $\vec{v}$ is the time derivative of the position vector:

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(D) The position vector of the ant is given by $\vec{S} = 2t^2 \hat{j} + 5 \hat{k}$.Velocity $\vec{v}$ is the time derivative of the position vector: $\vec{v} = \frac{d\vec{S}}{dt} = \frac{d}{dt}(2t^2 \hat{j} + 5 \hat{k}) = 4t \hat{j}$.At $t = 1 \ s$,the velocity is $\vec{v} = 4(1) \hat{j} = 4 \hat{j} \ m/s$.The magnitude of velocity is $|\vec{v}| = 4 \ m/s$.The direction is along the positive $y$-axis (indicated by the unit vector $\hat{j}$).

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

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Position of an ant ($S$ in metres) moving in $Y-Z$ plane is given by $S = 2t^2 \hat{j} + 5 \hat{k}$ (where $t$ is in seconds). The magnitude and direction of velocity of the ant at $t = 1 \ s$ will be:

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A
$16 \ m/s$ in $y$-direction
B
$4 \ m/s$ in $x$-direction
C
$9 \ m/s$ in $z$-direction
D
$4 \ m/s$ in $y$-direction

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3-2.Motion in Plane

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Motion In Two And Three Dimension

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$A$ hall has the dimensions $10\,m \times 12\,m \times 14\,m$. $A$ fly starting at one corner ends up at a diametrically opposite corner. What is the magnitude of its displacement in meters?

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$A$ 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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When is it necessary to use vectors?

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

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Write the equations of motion for uniformly accelerated motion in a plane.

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Position of an ant ($S$ in metres) moving in $Y-Z$ plane is given by $S = 2t^2 \hat{j} + 5 \hat{k}$ (where $t$ is in seconds). The magnitude and direction of velocity of the ant at $t = 1 \ s$ will be:

Similar Questions

$A$ hall has the dimensions $10\,m \times 12\,m \times 14\,m$. $A$ fly starting at one corner ends up at a diametrically opposite corner. What is the magnitude of its displacement in meters?

$A$ 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?

When is it necessary to use vectors?

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

Write the equations of motion for uniformly accelerated motion in a plane.

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