Question
A particle is moving such that its position co-ordinates $$\left( {x,y} \right)$$ are $$\left( {2m,3m} \right)$$ at time $$t = 0,\,\left( {6m,7m} \right)$$ at time $$t = 2\,s$$ and $$\left( {13m,14m} \right)$$ at time $$t = 5\,s.$$
Average velocity vector $$\left( {{v_{av}}} \right)$$ from $$t = 0$$ to $$t = 5\,s$$ is
A.
$$\frac{1}{5}\left( {13\hat i + 14\hat j} \right)$$
B.
$$\frac{7}{3}\left( {\hat i + \hat j} \right)$$
C.
$$2\left( {\hat i + \hat j} \right)$$
D.
$$\frac{{11}}{5}\left( {\hat i + \hat j} \right)$$
Answer :
$$\frac{{11}}{5}\left( {\hat i + \hat j} \right)$$
Solution :
Given, position vector of the particle at $$t = 0$$ is $$\left( {2\hat i + 3\hat j} \right)$$ and $$t = 5\,s$$ is $$\left( {13\hat i + 14\hat j} \right)$$
Average velocity vector $${v_{av}} = \frac{{{\text{Net displacement}}}}{{{\text{Time taken}}}}$$
$$\eqalign{
& = \frac{{\left( {13 - 2} \right)\hat i + \left( {14 - 3} \right)\hat j}}{5} \cr
& = \frac{{11\hat i + 11\hat j}}{5} \cr
& = \frac{{11}}{5}\left( {\hat i + \hat j} \right) \cr} $$