Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector quantity, meaning that both magnitude and direction are needed to define it (velocity vector). The scalar absolute value (magnitude) of velocity is called speed, a quantity that is measured in metres per second (m/s or m⋅s⁻¹) in the SI (metric) system. For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an acceleration.

The average velocity of an object over a period of time is its change in position, ${\displaystyle \Delta s}$, divided by the duration of the period, ${\displaystyle \Delta t}$, given mathematically as $${\displaystyle {\bar {v}}={\frac {\Delta s}{\Delta t}}.}$$

The instantaneous velocity of an object is the limit average velocity as the time interval approaches zero. At any particular time t, it can be calculated as the derivative of the position with respect to time: $${\displaystyle {\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {s}}}{\Delta t}}={\frac {d{\boldsymbol {s}}}{dt}}.}$$

From this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time (v vs. t graph) is the displacement, s. In calculus terms, the integral of the velocity function v(t) is the displacement function s(t). In the figure, this corresponds to the yellow area under the curve. $${\displaystyle {\boldsymbol {s}}=\int {\boldsymbol {v}}\ dt.}$$

Although the concept of an instantaneous velocity might at first seem counter-intuitive, it may be thought of as the velocity that the object would continue to travel at if it stopped accelerating at that moment.

While the terms speed and velocity are often colloquially used interchangeably to connote how fast an object is moving, in scientific terms they are different. Speed, the scalar magnitude of a velocity vector, denotes only how fast an object is moving, while velocity indicates both an object's speed and direction.

To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed.

For example, a car moving at a constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes. Hence, the car is considered to be undergoing an acceleration.