Kinematics: Describing Motion

velocity

Velocity is speed with a direction attached — it tells you not just how fast, but which way. '20 m/s' is a speed; '20 m/s due north' is a velocity. It answers the fuller question: how quickly, and in what direction, is the object's position changing? For anything that moves in a straight line and might go forwards or backwards, this direction is what lets you keep the two apart with a plus or a minus sign.

Precisely, velocity is the rate of change of position, and it is a vector. Average velocity over an interval is the displacement divided by the time: v = delta x / delta t. Because displacement carries direction, so does velocity. In one dimension a positive velocity means moving one way and a negative velocity the other; the size of the velocity is the speed. Its SI unit is metres per second (m/s).

Velocity is the bridge between position and acceleration: acceleration is defined as the rate at which velocity changes. Here is the crucial honesty: velocity changes whenever the speed changes or the direction changes, or both. A satellite in a circular orbit moves at constant speed but is always changing velocity, because it is always turning — and that changing velocity is exactly why it is accelerating even though its speed is fixed.

A ball rolls to the right at 3 m/s: velocity = +3 m/s. It bounces off a wall and rolls back left at 3 m/s: velocity = -3 m/s. The speed (3 m/s) never changed, but the velocity flipped sign because the direction reversed.

Same speed, opposite velocity: direction is what velocity adds on top of speed.

'Speed' and 'velocity' are used interchangeably in everyday talk but are different in physics: speed is a scalar (magnitude only), velocity is a vector (magnitude and direction). Constant speed does not imply constant velocity.

Also called
vvelocity vector