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Velocity: The rate in which an objects position is changing. Mathematically is the change in position divided by the time in which the position is changed.
An Alternative definition of velocity is displacement divided by time. Because displacement IS the change in an objects position, this definition is the same.
Velocity is also a Vector, meaning that IT MUST have a magnitude (size) and a direction. The magnitude of velocity is speed, so velocity has also been called speed with direction.