Physics · Motion In A Straight Line · NEET
No. It is the difference of the two velocities, and velocity carries a sign for direction. First fix a positive direction, then write v_A and v_B with their correct signs, and only then compute v_AB = v_A - v_B. If you subtract raw speeds without signs you will get the wrong answer whenever the two objects move in opposite directions.
The formula v_AB = v_A - v_B always subtracts. The subtraction itself handles both cases through the signs. If B moves opposite to A, then v_B is negative, and subtracting a negative number adds the magnitudes. So you never switch to a plus sign by hand; you just plug in the signed values and let the subtraction do the work.
'Velocity of A with respect to B' means: imagine you are standing on B and B feels stationary to you. How fast does A seem to move now? That apparent value is v_AB. The object after 'with respect to' is the one you pretend is at rest, and you subtract its velocity from everything.
Yes. If two cars both move at 60 km/h in the same direction, then v_AB = 60 - 60 = 0. To each driver the other car appears frozen in place, staying the same distance away. This zero relative velocity is why cars moving together on a highway seem still to each other.
They are equal in size but opposite in sign: v_AB = -v_BA. If A moves at +5 m/s relative to B, then B moves at -5 m/s relative to A. Always read the subscripts carefully in NEET questions, because they decide the sign of your final answer.
Buses leave cities X and Y in both directions at regular intervals of T minutes with the same speed. A girl driving from X to Y at 60 km/h notices that a bus moving in her direction passes her every 30 min, while a bus moving in the opposite direction passes her every 10 min. The interval T and the speed of the buses are respectively:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The velocity of A with respect to B is v_AB = v_A - v_B, where v_A and v_B are the signed velocities measured in the same reference frame along the same line.
It is a vector. In one dimension the direction is shown by the + or - sign, so v_AB has both a magnitude and a direction along the chosen axis.
For the same direction you subtract the magnitudes, and for opposite directions you add them. Both cases come out automatically from v_AB = v_A - v_B once you put in the correct signs.
Many NEET kinematics problems (trains crossing, buses passing, boats, lifts) are solved fastest by shifting to the frame of one object using relative velocity, which turns a two-body problem into a simple one-body problem.
It means the two objects keep a constant separation; each one sees the other as stationary. This happens when both move with equal velocities in the same direction.
