Adding Velocities

Rapidity: the hidden way speeds add

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Relativistic velocity addition: $w = \frac{u + v}{1 + uv/c^2}$.
• At low speeds it reduces to u + v.
• Rapidity $\phi$ with $\beta = \tanh\phi$: rapidities simply add.

Steps

1. Not simply adding
2. Half plus half
3. Rapidity
4. Stacking boosts
5. Nine-tenths plus nine-tenths
6. A year at 1 g