NEET Physics Two Dimensional Motion NEET PYQ-Two Dimensional Relative Motion

A particle is moving such that its position coordinates \[(x,\text{ }y)\] are \[(2m,\text{ }3m)\] at time \[t=0,\] \[(6m,\text{ }7m)\] at time \[t=2\text{ }s\] and \[(13m,\text{ }14m)\] at time \[t=5\text{ }s\]. Average velocity vector (\[{{\upsilon }_{a\upsilon }}\]) from \[t=0\] to \[t=5\,s\] is [NEET 2014]

A) \[\frac{1}{5}(13\mathbf{\hat{i}}+14\mathbf{\hat{j}})\]

B) \[\frac{7}{3}(\mathbf{\hat{i}}+\mathbf{\hat{j}})\]

C) \[2(\mathbf{\hat{i}}+\mathbf{\hat{j}})\]

D) \[\frac{11}{5}(\mathbf{\hat{i}}+\mathbf{\hat{j}})\]

Correct Answer: D

Solution :

Average velocity vector

\[{{v}_{av}}=\frac{\text{Net}\,\text{displacement}}{\text{Time}\,\text{taken}}\]

\[=\frac{(13-2)\mathbf{\hat{i}}+(14-3)\mathbf{\hat{j}}}{5}\]

\[=\frac{11\mathbf{\hat{i}}+11\mathbf{\hat{j}}}{5}=\frac{11}{5}(\mathbf{\hat{i}}+\mathbf{\hat{j}})\]