Illustration 2.1: Position and Displacement
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In physics we often talk about distance traveled and displacement to describe how the position of an object changes. Sometimes we even (appear to) use these terms interchangeably. However, they are not necessarily the same. Distance traveled is just that: the distance an object travels. The displacement of an object is a comparison of the final position to the initial position: Δx = x - x0, the distance displaced during the object's motion. Can you think of an example in which distance traveled and displacement are the same or different? Restart.
Shown are two animations, each with three toy monster trucks and their position vs. time graphs (position is given in centimeters and time is given in seconds). The arrow in each animation shows where the origin of coordinates is located. All measurements of position are with respect to this origin. Animation 1 shows the three monster trucks starting at different positions at t = 0 s. During this animation, for each individual truck, the distance traveled is equal to the displacement.
Note that we are treating each monster truck as an idealized object, a point. We are always measuring the position of a convenient part of the monster truck and then describing the motion of this part of the monster truck. For this animation the part of each monster truck that we follow is its front bumper, but it could have been the middle or the rear bumper. What matters is that we are consistent in the measurement process. The position of the object will vary depending on where you take the measurement (the front bumper, the middle, the rear bumper of the truck), but the difference in position measurements, the displacement vector, always stays the same. Therefore, it is not position that is important in physics, but rather the change in position or displacement that is important.
When you get a good-looking graph, right-click on it to clone the graph and resize it for a better view.
What are the average velocities of the trucks in Animation 1? Even though the trucks start at different positions, all three trucks have the same average speed (distance traveled/time) and average velocity (displacement/time). This can be seen from the slope of the graph (note that the distance traveled and displacements for each individual truck are identical in this animation). In Animation 2 the initial positions of the three monster trucks are the same, but each truck travels a different distance and also has a different displacement. The truck with the largest average speed and average velocity (for each individual truck, its average speed is still equal to its average velocity) is the one with the largest slope on the position vs. time graph.