Speed tells half the story. Two objects each traveling at 5 mph can remain stationary relative to one another or close their separation at 10 mph, because direction belongs to velocity even though it does not belong to speed. The distinction defeats intuition. A speedometer supplies a number; relative motion requires an arrow.
Stillness needs a reference. Consider two objects traveling east at 5 mph along parallel paths, with both speeds measured against the ground: their velocity vectors match, so subtracting one from the other gives zero relative velocity. Neither gains any ground. In a reference frame moving with either object, the other stays at the same position, although both continue changing position relative to the road. Direction changes the arithmetic. If one object instead travels west at 5 mph while the other travels east at 5 mph, their signed velocities differ by 10 mph; when they head directly toward one another, that difference is their closing speed.
Opposition alone proves less. Two objects moving in opposite directions can also separate at 10 mph, so an approach requires their positions, not merely their arrows, to put them on converging paths. Geometry keeps the accounts. At other angles, vector subtraction still determines relative velocity, but its magnitude need not equal the rate at which the distance between the objects shrinks. Nothing here contradicts motion. Under the Galilean transformation used for ordinary speeds, changing the observer changes the measured velocities without changing the encounter itself. The road slips backward; the neighboring object hangs motionless beside it.
