Relative Velocity Calculator
Calculate relative velocity using v_rel = v_A − v_B in 1D and relativistic cases.
What Is Relative Velocity Calculator?
The formula Calculate relative velocity using v_rel = v_A − v_B in 1D and relativistic cases., derives directly from fundamental physics principles.
Understanding this relationship enables both analytical calculation and intuitive reasoning about physical systems.
Applications span multiple fields of science and engineering. This calculator handles the arithmetic while you focus on the physics.
Ensure inputs are in SI units for correct results.
Formula Reference Table
| Solve For | Formula | Notes |
|---|---|---|
| Classical relative velocity | v_rel = v_A − v_B | Valid for v << c |
| Relativistic addition | v_rel = (v_A−v_B)/(1−v_A·v_B/c²) | Always < c |
| Same direction | v_rel = |v_A − v_B| | Approach speed (classical) |
| Opposite directions | v_rel = v_A + v_B | Closing speed (classical) — up to 2c possible! |
| Reference frame | Choose B as reference | v_rel = v_A as seen from B |
| Galilean (low speed) | v' = v − u | Velocity in moving frame |
3 Worked Examples
Car A at 120 km/h, B at 100 km/h in same direction.
- v_rel = 120-100 = 20 km/h (A pulls away at 20 km/h)
- In B's frame, A moves at 20 km/h forward
Train A at +80 km/h, Train B at -90 km/h.
- v_rel of A relative to B = 80-(-90) = 170 km/h
- They close at 170 km/h
Ship A: 0.8c, Ship B: 0.6c (same direction).
- v_rel = (0.8-0.6)/(1-0.8×0.6) = 0.2/0.52 = 0.385c
- Classical would give 0.2c — correct answer is 0.385c
Real-World Applications
Common Mistakes to Avoid
Use SI.
Check geometry/conditions.
Formula assumes ideal conditions.
Check conventions.
Verify squared/sqrt terms.
Frequently Asked Questions
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Interpretation: This relationship connects motion, force, momentum, work or energy in a mechanical system. Assumption: Choose a consistent reference direction and unit system. The model may assume constant acceleration, rigid bodies, negligible losses or an isolated system.