Velocity – defined; but it’s so much more complex
Velocity - A vector that measures the relative change in position of an object, and indicates the objects average direction.
scalar - A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction.
The magnitude of change in position in the case of this vector is a scalar. That magnitude may be calculated in many different ways. But in the motion of objects it is simple to calculate the difference between initial and current position. All other motion (the track of the position through time) is wasted motion. That track may be interesting in itself, however.
The direction is some what more complex than just a known heading - 23.4 degrees East of North. True north or magnetic north? In the case of our vector above the direction was an average direction indicative of the general direction based upon the initial position. Note that drawing a line through both end points of the line segment would also give a direction - slightly more toward the North (top of the page). Which is more accurate - neither. They are both valid measurements of the direction - the method of arriving at the direction is just slightly different. One could be considered an average heading (shown) - a better indication of trend toward a place. The other (line through end-point segments) is more of an instantaneous direction based on two data points. The former is reporting more accurately the trend over time, the latter more accurate direction if variance were to cease.
What is Velocity in the Agile / Scrum meaning?
Scrum team velocity is the amount of work effort completed and accepted by the Product Owner per Sprint (a rough measure of time) in the direction the Product Owner has steered the team (hopefully toward the Goal). It consist of two components - the scalar Story Points completed, and the direction. How one measures these two components is a blog posting for another time.