Momentum & Collisions · Physics

One-dimensional collisions: clean, fast, and test-friendly.

Head-on collisions reduce to a single axis. Use momentum conservation (and energy conservation for elastic cases) to solve for final speeds and directions.

This topic

One-Dimensional Collisions

Learn a reliable workflow and avoid sign mistakes with consistent direction conventions.

Core case

Head-on collisions

Everything happens along one axis — but directions matter.

Choose positive direction
Use signed velocities
Sanity checks on results

Solve it

Solving using conservation laws

Pick the right conservation statements for the collision type.

Momentum always (isolated system)
KE also for elastic collisions
KE loss for inelastic collisions

Shortcut

Relative velocity method (intro)

A fast method for 1D elastic collisions: relative speed of approach equals relative speed of separation.

When the method applies
How to set up the equation
Combine with momentum conservation

Practice

Practice & Exercises

Build automaticity for 1D collision setups.

Elastic collision speed-solve sets
Inelastic and perfectly inelastic problems
Sign-convention traps (practice)
Mixed “find type” questions
Exam-style multi-part collisions