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Find Displacement: Definition & Equation

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  • 0:01 Definitions & Properties
  • 1:28 Properties & Equation
  • 2:20 Examples of Displacement
  • 4:12 Lesson Summary
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Lesson Transcript
Instructor
Richard Cardenas

Richard Cardenas has taught Physics for 15 years. He has a Ph.D. in Physics with a focus on Biological Physics.

Expert Contributor
Wiley Iverstine

Wiley Iverstine holds master’s degree in natural science from Louisiana State University and spent 27 years teaching DE, AP, Regular & Honors Chemistry/Physics.

In this lesson, you will learn about displacement, the properties associated with it, the equation needed to calculate displacement, and some simple examples of the calculations.

Definitions & Properties

You start from home, drive to the grocery store that is 20 miles away, then back home. You traveled a distance of 40 miles for the round trip, but your displacement was zero for the round trip. Displacement and distance are two quantities that need to be defined in order for each quantity to be fully understood. Also, we can't talk about displacement without comparing it to distance.

Consider this figure (see video), which shows three different paths between points A and B.

Three Paths from Point A to Point B
MultiPath

Path 1 covers the greatest distance, and Path 2 covers the least distance. However, all three paths have the same displacement. This is because distance refers to the actual length of the path taken by an object. Even though all three paths begin and end at the same spot, each path covers a different distance. Distance is a scalar quantity, so it is always a positive number with no regard for what direction the object is moving. So, for any path, the distance covered always gets bigger.

Displacement, however, refers to the difference between the final position and the initial position of a path taken by an object. So, what the figure above illustrates is that displacement does not care what happens between the start and end points of a path; all that matters is the distance between the start and end points of the path.

Properties & Equation for Displacement

Displacement is a vector quantity, which means that we need to specify a magnitude and direction. So, unlike distance, displacement cares what direction the object is going when it moves between two points. So, in one dimension, displacement can be positive, negative, or zero. Remember, displacement depends on the initial and final positions of the path taken by an object.

This is the formula for displacement:

Displacement

Delta x (or delta y) is the mathematical symbol for displacement. The delta refers to a change. In this case, the change refers to the distance between the final and initial positions of the object. Let's look at some different examples and use the formula to calculate the displacement of objects as they move between points on a path to put everything into perspective.

Examples of Displacement

Consider the path shown in this figure. Assume the distances marked in the figure are in meters.

Positive

The final position is 5 meters, and the initial position is 0 meters. Using the formula, we can calculate the displacement as 5 meters minus 0 meters, which equals 5 meters. In this case, the distance covered is also 5 meters. The displacement in this figure is 5 meters.

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Additional Activities

Practicing Position

To better understand the idea of displacement, students need to apply the concepts of position (positive and negative). Find a room or area outside large enough for everyone to move around freely without bumping into one another. The following agreements must be understood:

1. All motion must be in the same plane; so choose either north/south or motion long a road or building, something the students can continually relate to. It is confusing to add a second dimension at this point.

2. Establish a reference or "0" from which all positions can be measured; preferably a clear maker at the center of the area.

3. Positive positions are ones to the right of the reference to the observer; since this will change for each observer to establish one observation point for everyone. An example would be to say all positions north of reference are positive.

Now choose a few objects throughout the area and have the students measure the position of each object relative to the reference point. As an example say the following is a picture of the area you are using. The blue circle in the middle represents a pole close to the center of your area. Notice that the 0 on the reference line is aligned with the center of the pole. Discuss this with your students and make sure they understand this is a reference or the point at which all measurements are made from. Next state that all motions are along the length of the fence and motions away from the building or to the right are positive. Finally, choose a clearly definable position and have students measure that position.

A good example would be to have them measure to the last picket on the fence away from the building. Students will complete this with meter sticks but according to our number line they should come up with a +6.3 m. Remind them that they should always measure to the center of an object and that the positive means that the object is to the right of the reference according to the Observer. Next, you may have them measure to the position of the building. According to our number line, their answer should be -5.0 m. The negative means that the building is to the left of the reference according to the Observer.

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