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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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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.

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.

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.

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.

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:

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.

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

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.

Now, consider the path shown in this next figure.

The final position is 0 meters, and the initial position is 5 meters. The displacement is 0 meters minus 5 meters, giving us a displacement of -5 meters. The displacement in this case is negative. The distance covered in this example is still 5 meters.

Moving on, let's consider the more complex motion along the path shown in this figure.

The final position is -3 meters, and the initial position is 0 meters. The displacement is calculated as -3 meters minus 0 meters, which equals -3 meters. The distance covered in this example is 13 meters (5 meters right + 8 meters left).

Finally, consider the path shown in this last figure:

The final position is 0 meters, and the initial position is 0 meters. This gives us a displacement of 0 meters. In this example, the distance covered is 10 meters. This means that your displacement is always 0 whenever you end up back where you started. So, whenever you drive to work in the morning and return home from work in the evening, your displacement for the day is 0 meters.

Let's review. **Displacement** is a vector quantity, so we need to specify a magnitude and direction in order to fully characterize it. Unlike **distance**, which can only get larger on any path taken, displacement can be positive, negative, or zero. Displacement is zero when you start and end at the same spot. As we saw in the examples, the distance and displacement covered in different paths are rarely the same number, which is basically due to the fact that distance is a **scalar quantity** and displacement is a **vector quantity**. Finally, displacement only depends on where you begin and end; it does not matter what you did in between. Displacement is path independent.

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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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