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(D) At time $t_1 = 0 \, s$,the position vector of the particle is $\vec{r}_1 = 2\hat{i} + 3\hat{j}$.At time $t_2 = 5 \, s$,the position vector of the

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

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(D) At time $t_1 = 0 \, s$,the position vector of the particle is $\vec{r}_1 = 2\hat{i} + 3\hat{j}$.At time $t_2 = 5 \, s$,the position vector of the particle is $\vec{r}_2 = 13\hat{i} + 14\hat{j}$.The displacement $\Delta \vec{r}$ from $t = 0$ to $t = 5 \, s$ is given by $\Delta \vec{r} = \vec{r}_2 - \vec{r}_1$.$\Delta \vec{r} = (13\hat{i} + 14\hat{j}) - (2\hat{i} + 3\hat{j}) = 11\hat{i} + 11\hat{j}$.The average velocity $\vec{v}_{av}$ is defined as the total displacement divided by the total time interval $\Delta t = t_2 - t_1 = 5 - 0 = 5 \, s$.$\vec{v}_{av} = \frac{\Delta \vec{r}}{\Delta t} = \frac{11\hat{i} + 11\hat{j}}{5} = \frac{11}{5}(\hat{i} + \hat{j}) \, m/s$.

Column $I$	Column $II$
$(A)$ Average velocity between initial and final points	$(p)$ $u \sin \theta$
$(B)$ Change in velocity between initial and final points	$(q)$ $u \cos \theta$
$(C)$ Change in velocity between initial and highest points	$(r)$ Zero
$(D)$ Average velocity between initial and highest points	$(s)$ None of the above

$A$ particle is moving such that its position coordinates $(x, y)$ are $(2 \, m, 3 \, m)$ at time $t = 0$,$(6 \, m, 7 \, m)$ at time $t = 2 \, s$,and $(13 \, m, 14 \, m)$ at $t = 5 \, s$. The average velocity vector $\vec{v}_{av}$ from $t = 0$ to $t = 5 \, s$ is:

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