Question:
The velocity vector of the motion described by the position vector of a particle, $\vec{r}=\left(2 t \hat{i}+t^{2} \hat{j}\right)$ is given by
The velocity vector of the motion described by the position vector of a particle, $\vec{r}=\left(2 t \hat{i}+t^{2} \hat{j}\right)$ is given by
Updated On: Jun 14, 2022
- $ \vec{v} = (2\hat{i}+2t\,\hat{j}) $
- $ \vec{v} = (2t\,\hat{i}+2t\,\hat{j}) $
- $ \vec{v} = (t\,\hat{i}+t^2\,\hat{j}) $
- $ \vec{v} = (2i+t^2\,\hat{j}) $
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The Correct Option is A
Solution and Explanation
Given $r=2 t \hat{i}+t^{2} \hat{j}$
Velocity vector $v=\frac{d r}{d t}$ and using
$\frac{d}{d x} x^{n}=n x^{n-1}$
We have, $\frac{d r}{d t}=2 \hat{i}+2 t \hat{j}$
Velocity vector $v=\frac{d r}{d t}$ and using
$\frac{d}{d x} x^{n}=n x^{n-1}$
We have, $\frac{d r}{d t}=2 \hat{i}+2 t \hat{j}$
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration