1. Consider two trains A and B moving on two parallel tracks in the same direction.

2. Case 1: Train B overtakes train A.

For a passenger in train A, train B appears to be moving slower than train A. This happens because the passenger in train A perceives the velocity of train B with respect to him/her i.e., the difference in the velocities of the two trains which is much smaller than the velocity of train A.

3. Case 2: Train A overtakes train B.

For a passenger in train A, train B appears to be moving faster than train A. This happens because the passenger in train A perceives the velocity of the train B w.r.t. to him/her i.e., the difference in the velocities of the two trains which is larger than the velocity of train A.

4. If \(\overset\rightarrow{v}_A\) and \(\overset\rightarrow{v}_B\) be the velocities of two bodies then relative velocity of A with respect to B is given by \(\overset\rightarrow{v}_{AB}=\overset\rightarrow{v}_A-\overset\rightarrow{v}_B.\)

5. Similarly the velocity of B with respect to A is given by, \(\overset\rightarrow{v}_{AB}=\overset\rightarrow{v}_B-\overset\rightarrow{v}_A.\)

Thus, relative velocity of an object w.r.t. another object is the difference in their velocities

6. If two objects start form the same point at t = 0, with different velocities, distance between them increases with time in direct proportion to the relative velocity between them.