velocity

Velocity answers the question: how fast is something moving, and in what direction? In one dimension, it is a single signed number — positive for motion to the right, negative for motion to the left. In two or three dimensions, velocity is a vector, carrying both a speed (its magnitude) and a direction. It is distinct from speed, which is the magnitude of velocity and always positive.

Mathematically, velocity is the time derivative of position: v = dx/dt. If you plot position against time, the velocity at any instant is the slope of the tangent line at that point. A horizontal line on a position-time graph means zero velocity — the object is at rest. A steep line means fast motion. A line that curves upward means velocity is increasing, which is acceleration.

The SI unit of velocity is metres per second. Other common units include kilometres per hour, miles per hour, and the more specialised knots (nautical miles per hour, used in navigation and aviation). For everyday motion, these are interchangeable through simple conversion factors. For cosmic motion — galaxies receding, stars orbiting — astronomers use kilometres per second, and for light and gravitational waves, the natural unit is the fraction of c.

Velocity is the bridge between position and acceleration. Integrate acceleration over time and you recover velocity. Differentiate position over time and you recover velocity. It sits in the middle of the derivative chain, and almost every law of motion — Newton's second, the work-energy theorem, the momentum principle — is written in terms of it.