EQUATION

Relative Velocity (1D, Head-On)

Gives the closing speed of two objects moving directly toward each other

§ 01

The equation

EQ.RELATIVE-VELOCITY-1D
v_{close} = v_A + v_B
§ 02

What it solves

Gives the closing speed of two objects moving directly toward each other. The time to collision is then the initial gap divided by this combined speed.

§ 03

When to use it

One-dimensional collisions or meetings where both objects approach each other. Also applies (with subtraction) when one object overtakes another moving in the same direction.

§ 04

When NOT to use it

Does not apply to 2D encounters — use vector subtraction there. Fails at relativistic speeds, where velocities add by the Lorentz formula, not simple arithmetic.

§ 05

Common mistakes

Adding velocities for same-direction motion instead of subtracting. Forgetting to define a consistent positive direction before writing signs. Using ground-frame speeds when the problem asks for the speed of A relative to B's reference frame.

§ 06

Topics that use this equation

§ 07

Problems using this equation