The notion of vector in three dimensional space is one of the important concepts used in the mathematical description of physical entities. The velocity of a piece of matter has a direction and a magnitude; it is a vector. The force that is exerted at a point of a body is also a vector. In this chapter we shall be concerned only with two kinds of vectors, the “velocity vector” and the closely related “momentum vector”.

Different portions of a piece of matter—referred to as a “body”—may have different velocities. We shall assume that this is not so for the bodies to be considered in the present chapter; that is to say, we shall assume that all parts of the body move with the same velocity. When this is the case, the body is frequently imagined to be concentrated at a single mathematical point (at its center of gravity, for example) and is called a “particle”. This single point serves as initial point of the velocity vector.

Before numerical quantities can be assigned to the motion of a body, a unit of length and a unit of time must be selected; we assume that this has been done.

Suppose now a body moves in a definite direction. During an interval of time it will cover a certain distance.