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⚛️ NEET Physics❓ Question

Two trains crossing each other: when do I add speeds and when do I subtract? And the v_AB sign thing

Sara Fernandes11th Sample

9 Oct 2026 · 1 min read

Football practice got cancelled so I decided to be productive and do relative velocity. It did not go well.

Here's the problem. Train A is 100100 m long, train B is 150150 m long, on parallel tracks.

(a) They move in opposite directions at 2020 m/s and 3030 m/s. How long to cross each other completely? (b) They move in the same direction at 3030 m/s (B, behind) and 2020 m/s (A, ahead). How long does B take to completely overtake A?

My answer for (a): relative speed =20+30=50= 20+30 = 50 m/s, distance =250= 250 m, time =5=5 s. For (b) I subtracted: 1010 m/s, time =25=25 s. The answer key agrees but I kind of did this by instinct and not logic.

What I don't get is the formula vAB=vA−vBv_{AB} = v_A - v_B in NCERT. Is that "velocity of A relative to B"? Sometimes I write vB−vAv_B - v_A and get a negative time or something. How do I decide which sign to use, and does it really matter?

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7 answers & replies

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  • [+]Ishaan Bose11thSample· 10d ago

    Your instinct is right so keep that. Here's the logic: pick one train as your "home", imagine you're sitting in it and watching the other. In (a) from train A you see B approach at 20+30=5020+30=50 m/s because they come from opposite sides. In (b) from B you see A moving away at 30−20=1030-20=10 m/s... actually that A "falls back" at 10 m/s relative to you. The overtaking is complete when the back of B passes the front... no wait, front of B passes the back of A... you need relative displacement of the sum of lengths.

    • [+]Neel Chatterjee12thSample· 10d ago

      Ishaan, careful, it's for overtaking: the rear of B (faster) must go past the front of A, so B has to gain the full 100+150=250100+150=250 m on A. Relative speed 1010 m/s so t=25t=25 s. Sara got it right. For "crossing" or "overtaking" both cases the relative distance is the sum of lengths.

      • [+]Ishaan Bose11thSample· 10d ago

        Yeah my brain collapsed mid-sentence lol. Sum of lengths. Moving on.

  • [+]Arjun Nair12thSample· 10d ago

    On the sign convention: vAB=vA−vBv_{AB} = v_A - v_B means "velocity of A as seen from B". Choose a positive direction first, put signs on both velocities, then subtract. Example (a): take B's direction as positive. Then vB=+30v_B=+30 and vA=−20v_A=-20. So vAB=−20−30=−50v_{AB}=-20-30=-50 m/s, A moves at 50 m/s in the negative direction as seen from B. The magnitude is 50, which is what time needs. vBA=+50v_{BA}=+50. Opposite sign, same magnitude: vBA=−vABv_{BA} = -v_{AB}.

    So it doesn't matter for time questions (magnitude only), but it matters when asked for the direction or in graph / sign-based questions.

    • [+]Sara Fernandes11thSample· 10d agoAuthor

      Right, so choose the positive direction, give signs, subtract, and read the magnitude. This is going into my notebook, thank you all!

  • [+]Vivek Mishra12thSample· 10d ago

    A common mistake in this type of problem: people also use the length of only one train. Check whether the question says "crosses a pole/man" (only one train's length) or "crosses another train" (both lengths added). I lost two marks like this last year.

  • [+]Kavya NaikDropperSample· 10d ago

    One more: in a river problem in 1D where a boat goes along the flow, the speed relative to the ground is boat + river. Against the flow, boat - river. But careful, it's the flip of the trains rule: for ground speed, same direction → add, opposite → subtract (seeing one body from another it's the reverse). Everything is just relative velocity.

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