Question

A particle is moving such that its position coordinate $(x,y)$ are $(2\text{m},3\text{m})$ at time $t=0,$ $(6\text{m},7\text{m})$ at time $t=2\text{s}$ and
$(13\text{m},14\text{m})$ at time $t=5\text{s}$
Average velocity $\left({\overrightarrow{V}}_{av}\right)$ from $t=0$ to $t=5\text{s}$ 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 1

The correct option is D $\frac{11}{5}(\hat{i}+\hat{j})$

Average velocity is defined as rate of change of displacement.
Given initial position is $r_1=2\hat{i}+3\hat{j}$
and at $t=5\text{s}$ final position is $r_2=13\hat{i}+14\hat{j}$

Average velocity
${\overrightarrow{v}}_{av}=\frac{\Delta \overrightarrow{r}}{\Delta t}=\frac{(13-2)\hat{i}+(14-3)\hat{j}}{5-0}=\frac{11}{5}(\hat{i}+\hat{j})\text{m/s}$