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 $t=2\text{s}$.

• A. $5\text{m/s}$
• B. $20\text{m/s}$
• C. $10\text{m/s}$
• D. $28\text{m/s}$

Answer 1

The correct option is B $20\text{m/s}$

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

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

$\overrightarrow{v}=8t\hat{i}+6t\hat{j}$
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.