Relative Velocity (1D, Head-On)
Gives the closing speed of two objects moving directly toward each other
The equation
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.
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.
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.
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.