Relative motion in one dimension

Velocity of A relative to B: v_AB = v_A − v_B. Subtract velocities, never add them blindly.

Relative motion in one dimension0 min · Free lecture

In this lesson

  • Velocity of A relative to B: v_AB = v_A − v_B. Subtract velocities, never add them blindly.

Two trains at 60 km/h and 40 km/h: approaching at 100, separating at 20. One formula.

v_AB = v_A − v_B is the velocity of A as seen from B's frame. Opposite directions → speeds add; same direction → speeds subtract.

Relative motion converts chasing problems into rest problems: fix B's frame, and A just moves at v_AB with the separation as the initial gap.

vA/B=vA−vBv_{A/B} = v_A - v_B

Relative velocity in 1D

Worked example

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.

  1. Area under the a–t graph = change in velocity.
  2. Area = 2 m/s² × 4 s = 8 m/s (the last 2 s add nothing).

Answer: 8

Transcript (0 min)
WEBVTT

1
00:00:00.000 --> 00:00:05.000
Relative motion in one dimension — FemtoLearn.
2
00:00:05.000 --> 00:00:15.000
Velocity of A relative to B: v_AB = v_A − v_B. Subtract velocities, never add them blindly.
Printable notes (free)

Practice

Free · 4 questions with full solutions
  1. Q1 · 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.

  2. Q2 · 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
  3. Q3 · 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.

  4. Q4 · MCQ · difficulty 2/5

    The slope of a velocity–time graph gives:

    • Displacement
    • Acceleration
    • Speed
    • Distance