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

• A. $\vec{v} = (2\hat{i}+2t\,\hat{j})$
• B. $\vec{v} = (2t\,\hat{i}+2t\,\hat{j})$
• C. $\vec{v} = (t\,\hat{i}+t^2\,\hat{j})$
• D. $\vec{v} = (2i+t^2\,\hat{j})$

Answer 1

Answer: (A)

$\vec{v} = (2\hat{i}+2t\,\hat{j})$

Answer 2

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, $\frac{d r}{d t}=2 \hat{i}+2 t \hat{j}$