Position and Displacement

The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference, and we often describe the position of an object as it relates to stationary objects on Earth. For example, a rocket launch could be described in terms of the position of the rocket with respect to Earth as a whole. On the other hand, a cyclist's position could be described in terms of where they are in relation to the buildings they pass. In other cases, we use reference frames that are not stationary but are in motion relative to Earth. To describe the position of a person in an airplane, for example, we use the airplane, not Earth, as the reference frame. To describe the position of an object undergoing one-dimensional motion, we often use the variable x.

If an object moves relative to a frame of reference, then the object's position changes. For example, if a professor moves to the right relative to a whiteboard, then the professor's position has changed. This change in position is called displacement. The word displacement implies that an object has moved or has been displaced. Although the position is the numerical value of x along a straight line where an object might be located, displacement gives the change in position along this line. Since displacement indicates direction, displacement is a vector quantity and can be either positive or negative, depending on which direction is chosen as positive.

Also, an analysis of motion can have many displacements embedded in it. For example, if the right is positive, and an object moves 2 m to the right, then 4 m to the left, the individual displacements are 2 m and −4 m, respectively. Displacement is denoted by Δx, which is the change in position. We always solve for displacement by subtracting the initial position from the final position.

This text is adapted from Openstax, University Physics Volume 1, Section 3.1: Position, Displacement, and Average Velocity.