Previous Year NEET Question- Optics L-8

Question: A particle is moving such that is position coordinates $(x, y)$ are $(2 \mathrm{~m}, 3 \mathrm{~m})$ at time $t=0$, $(6 \mathrm{~m}, 7 \mathrm{~m})$#

at time $\mathrm{t}=2 \mathrm{~s}$ and $(13 \mathrm{~m}, 14 \mathrm{~m})$ at time $\mathrm{t}=5 \mathrm{~s}$. Average velocity vector $\left(\vec{v}_{a v}\right)$ from $t=0$ to $t=5 \mathrm{~s}$ is

A) $\frac{1}{5}(13 \hat{i}+14 \hat{j})$

B) $\frac{7}{3}(\hat{i}+\hat{j})$

C) $2(\hat{i}+\hat{j})$

D) $\frac{11}{5}(\hat{i}+\hat{j})$

Answer: $\frac{11}{5}(\hat{i}+\hat{j})$#

Sol:#

$\begin{aligned} & \overrightarrow{v_{a v}}=\frac{\Delta \vec{r} \text { (displacement) }}{\Delta t \text { (time taken) }} \ & =\frac{(13-2) \hat{i}+(14-3) \hat{j}}{5-0}=\frac{11}{5}(i+j) \end{aligned}$