Velocity is a vector quantity that describes the rate at which an object changes its position with respect to time. It specifies both the speed and direction of an object's motion. In physics, velocity is a fundamental concept used to describe the motion of objects and is an important parameter in understanding the dynamics of various physical systems.

Mathematically, velocity (v) is defined as the change in displacement (Δx) of an object divided by the change in time (Δt) over which the displacement occurs:

Velocity (v) = Δx / Δt

where:

• v is the velocity of the object (a vector quantity),
• Δx is the change in displacement of the object (the final position minus the initial position), and
• Δt is the change in time over which the displacement occurs (the final time minus the initial time).