Position

In order to describe the motion of an object or body, you must first be able to describe its position—where it is at any particular time. More precisely, you need to specify its position relative to a convenient reference frame. Earth is often used as a reference frame, and we often describe the position of an object as it relates to stationary objects in that reference frame. For example, a high jump would be described in terms of the position of the jumper with respect to the Earth as a whole, while a professor’s position could be described in terms of where she is in relation to the nearby white board.  In other cases, we use reference frames that are not stationary but are in motion relative to the Earth. To describe the position of a person in an airplane, for example, we use the airplane, not the Earth, as the reference frame. In biomechanics, we typically agree on a reference frame relative to an origin. If we are describing motion based off a picture or video, we use the bottom left-hand corner as our origin and describe movement relative to that point.Please see the figures 2 and 3 below.

Displacement

If an object moves relative to a reference frame (for example, if a professor moves to the right relative to a white board or a passenger moves toward the rear of an airplane), then the object’s position changes. This change in position is known as displacement. The word “displacement” implies that an object has moved, or has been displaced.

Note that displacement has a direction as well as a magnitude. The professor’s displacement is 2.0 m to the right, and the airline passenger’s displacement is 4.0 m toward the rear. In one-dimensional motion, direction can be specified with a plus or minus sign. When you begin a problem, you should select which direction is positive (usually that will be to the right or up, but you are free to select positive as being any direction). The professor’s initial position is p_xi = 1.5 m and her final position is p_xf = 3.5 m. Thus her horizontal displacement is

 [latex]\Delta\overrightarrow{\mathbf{p_x}} = \overrightarrow{\mathbf{p_{xf}}} - \overrightarrow{\mathbf{p_{xi}}} = 3.5 \textbf{ m} - 1.5 \textbf{ m} = +2.0 \textbf{ m}[/latex]

In this coordinate system, motion to the right is positive, whereas motion to the left is negative. Similarly, the airplane passenger’s initial position is p_xi = 6.0 m and his final position is p_xf = 2.0 m, so his displacement is

 [latex]\Delta\overrightarrow{\mathbf{p_x}} = \overrightarrow{\mathbf{p_{xf}}} - \overrightarrow{\mathbf{p_{xi}}} = 2.0 \textbf{ m} - 6.0 \textbf{ m} = -4.0 \textbf{ m}[/latex]

Distance

Although displacement is described in terms of direction, distance is not. Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between two positions is not the same as the distance traveled between them. Distance traveled is the total length of the path traveled between two positions. Distance has no direction and, thus, no sign. For example, the distance the professor walks is 2.0 m. The distance the airplane passenger walks is 4.0 m.