The position of a body in space is denoted by its three coordinates x, y and z. To specify the position of a body, we use a reference point with respect to a set of axes.
The set of axes consists of three mutually perpendicular lines labelled as the x, y and z axes. The point of intersection of these three axes is called the origin. To specify the position of a body, its x, y and z coordinates are given with respect to this rectangular coordinate system. A stop watch is included to complete the frame of reference.
When any one or more of the coordinates change with time, the body is said to be in motion with respect to the frame of reference. When the coordinates don’t change with time, the body is said to be at rest with respect to the frame of reference. Rest and motion are relative terms, and are always specified with respect to the frame of reference.
Positions to the right of O are taken as positive and to the left of O as negative. Positions above O are taken as positive and below O as negative. With time, the position of the body changes and describes a path.
The path length and displacement of a body depend on how its position changes with time. Path length is the distance traversed by a body, whereas displacement is the change in the position of the body. The path length is a scalar quantity as it has only magnitude and no direction. Since displacement has magnitude and direction, it is a vector.
The magnitude of displacement and the path length traversed by an object may or may not be the same. There may be cases where the displacement of an object may be zero even though it has moved, but its path length will not be zero.