Explain the concept of relative velocity along a straight line with the help of an example.
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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.
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