Relative velocity: same and opposite directions

Same direction: subtract. Opposite directions: add. Then crossing times are trivial.

Relative velocity: same and opposite directions0 min · Free lecture

In this lesson

  • Same direction: subtract. Opposite directions: add. Then crossing times are trivial.

Overtaking is just relative motion with the gap as distance.

Same direction: v_rel = v_fast − v_slow; time to overtake = gap/v_rel. Opposite: v_rel = v₁ + v₂; crossing time = total length/v_rel.

This is the entire physics of train-crossing and overtaking problems — everything else is arithmetic.

tcross=L1+L2v1+v2t_{cross} = \frac{L_1 + L_2}{v_1 + v_2}

Trains crossing in opposite directions

Worked example

A body moves with v = 10 m/s for 3 s, then v = 5 m/s for 2 s in the same direction. Find the total distance.

  1. Distance = area under the v–t graph.
  2. 10×3 + 5×2 = 30 + 10 = 40 m.

Answer: 40

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Relative velocity: same and opposite directions — FemtoLearn.
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Same direction: subtract. Opposite directions: add. Then crossing times are trivial.
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Practice

Free · 4 questions with full solutions
  1. Q1 · Numerical · difficulty 2/5

    A body moves with v = 10 m/s for 3 s, then v = 5 m/s for 2 s in the same direction. Find the total distance.

  2. Q2 · Numerical · difficulty 2/5

    The acceleration of a body starting from rest is a = 2 m/s² for 4 s, then zero for 2 s. Find its velocity at t = 6 s.

  3. Q3 · MCQ · difficulty 2/5

    A particle moves with constant velocity. Which a–t graph describes it?

    • A horizontal line at a = 0
    • A horizontal line at a = 2 m/s²
    • A straight line through the origin
    • A parabola
  4. Q4 · MCQ · difficulty 2/5

    The slope of a velocity–time graph gives:

    • Displacement
    • Acceleration
    • Speed
    • Distance