Question

The position vector of a particle is given as $\overrightarrow r=4t^2~\hat{i}+3t^2~\hat{j}$ (in $\text {meters}$).
Find the magnitude of instantaneous velocity at $t=2~\text s $.

Answer 1

Given,
$\overrightarrow r=4t^2~\hat{i}+3t^2~\hat{j}$
We know that,
$\overrightarrow v=\dfrac{d\overrightarrow r}{dt}$

$\overrightarrow v=\dfrac {d(4t^2~\hat{i}+3t^2~\hat{j})}{dt}$

$\overrightarrow v=8t~\hat{i}+6t~\hat{j}$
at $t=2~\text s$,
$\overrightarrow v=16~\hat{i}+12~\hat{j}$

Magnitude of velocity at $t=2~\text s$,
$|\overrightarrow v|=\sqrt{16^2+12^2}=20~\text {m/s}$

Hence, option $\text {(B)}$ is the correct answer.