Chapter 2: Describing Movement in One Dimension, 1-D Linear Kinematics (10/45) -- Introduction to Biomechanics

Chapter 2: Describing Movement in One Dimension, 1-D Linear Kinematics 2.1 Displacement Authors: Paul Peter Urone, Roger Hinrichs Adapted by: Rob Pryce, Alix Blacklin Learning Objectives By the end of this section, you will be able to: - Define position, displacement, distance, and distance traveled. - Explain the relationship between position and displacement. - Distinguish between displacement and distance traveled. - Calculate the displacement and distance given initial position, final position, and the path between the two. Position In order to describe the motion of a person (or any object for that matter), you must first be able to describe their position—where they are at any particular time. More precisely, position is defined as the location in space relative to a specific reference frame. A reference frame is an arbitrary location (or origin) and set of axes from which the position and motion of an object can be described. Earth is often used as a reference frame, and we often describe the position of a person or object as it relates to the Earth or to stationary objects in the Earth reference frame. For example, a high jumper’s motion would be described in terms of the position of the person with respect to the Earth (or more specifically, the ground level they jumped from). While a professor’s position during a lecture could be described in terms of where she is in relation to the nearby white board (Figure 2.3). 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 (Figure 2.4). Or more commonly in biomechanics, we might describe the motion of one athlete with respect to another athlete – in this case, the reference is other athlete and we can calculate position, displacement or velocity of other athletes relative to them. That is, how far in front or behind they are, how quickly they are catching up or falling behind, and so on. To describe the position of a person or object that is undergoing movement in 1-dimension (e.g. forwards or backwards), we often use the variable [latex]x[/latex], particularly if the motion is in the horizontal direction. In the next chapter, during the discussion of free fall, the variable [latex]y[/latex] will be used to describe motion in the vertical direction. In the next section we’ll learn about axes in the reference frame. 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. Displacement is calculated as: [latex]\Delta x = x_f - x_i[/latex] where [latex]\Delta x[/latex] is displacement, and [latex]x_f[/latex] is the final positi