Physics · Motion In A Straight Line · NEET
You SUBTRACT. Give both velocities a sign first (say rightward is +). If car A moves at +80 km/h and car B at +60 km/h, then velocity of B relative to A is v_BA = v_B − v_A = 60 − 80 = −20 km/h. The size is only 20 km/h because they are chasing each other, so they separate slowly. The minus sign just tells you B falls behind A.
Because they have opposite signs. Take rightward as +. If A moves at +80 km/h and B moves at −60 km/h (leftward, towards A), then v_BA = v_B − v_A = (−60) − (+80) = −140 km/h. The magnitude is 80 + 60 = 140 km/h. The formula is always v_BA = v_B − v_A; the addition happens automatically once you put in the correct signs. That is why opposite-direction relative speed is large.
Closing speed (or approach speed) is just the magnitude of the relative velocity along the line joining them, and it tells how fast the gap shrinks. Same direction: gap closes at |v1 − v2|. Opposite direction (moving towards each other): gap closes at v1 + v2. Time to meet = initial gap / closing speed. Relative velocity has a sign and direction; closing speed is the positive number you use for 'when do they meet'.
No, they are opposite in sign but equal in size. v_AB = velocity of A as seen by B = v_A − v_B. v_BA = velocity of B as seen by A = v_B − v_A. So v_AB = −v_BA. Read the order right-to-left: v_BA means 'B relative to A'. For NEET, decide whose frame you are sitting in, then subtract that person's velocity from everything else.
Zero. If v_A = v_B (same speed, same direction), then v_BA = v_B − v_A = 0. In A's frame, B looks frozen and the distance between them never changes. This is why two cars at the same speed on a highway seem to 'stand still' relative to each other.
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.
Velocity of B with respect to A is v_BA = v_B − v_A, where v_A and v_B are taken WITH their signs on a chosen axis. Same direction gives a subtraction; opposite direction makes the terms add up in magnitude.
It is a vector. In one dimension the 'direction' is carried by the + or − sign. Always fix a positive direction first, put signs on every velocity, then apply v_BA = v_B − v_A.
Time to meet = initial distance between them / relative (closing) speed. Use v1 + v2 if they move towards each other and |v1 − v2| if they move the same way. This is the fastest NEET shortcut and avoids solving two position equations.
When both move the same way their motions partly cancel, so only the difference in speeds remains. When they move opposite ways the speeds combine, so the gap changes much faster. This is why an overtaking train seems slow but an oncoming train flashes past.
