Lesson Video: Displacement Science

In this video, we will learn how to distinguish the distance that an object moves between two points from the displacement of the object between those points.

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Video Transcript

In this video, we will learn how to distinguish the distance that an object moves between two points from the displacement of the object between those points. The terms distance and displacement are related.

Before getting to displacement, let’s talk first about distance. Say that we have two points. We’ll call them our starting and ending locations. To get from the start to the end point, we could travel in a straight line like this. This is the shortest possible distance between these points. We could also move from the start to the end by, say, first moving upward then over to the right and down to the end point. Even though both these paths start and end at the same locations, they cover different amounts of distance. Distance is the length of the path traveled between two points. Knowing this, let’s look at a quick example.

A car is at the center of a circle. The arrows show paths that the car could travel to reach the circumference of the circle. Is the distance moved the same for both paths? Yes or no.

We see that for both the blue and the red arrows, the start and end point of these arrows is the same. However, the red arrow, because it is curved, indicates a longer path between these points. The distance between two points is defined as the length of the path traveled between them. Since the red path is longer than the blue path, the distance moved is not the same for both paths.

Now that we know what distance is, let’s move on to displacement. Once again, we have our start and end points. The pink arrow indicates the displacement from start to end. The length of the arrow tells the magnitude or size of the displacement, and the direction of the arrow indicates the direction of travel. Both a magnitude and a direction are needed to define displacement. This means that displacement is a vector. It’s the straight-line distance between two points in the direction of travel.

Recall that this is different from distance, which is the length of path traveled between two points. While displacement is a vector, so it does tell us about direction, distance is a scalar, so it does not. Let’s now look at a few more examples.

A car drives along a circular path, returning to the point from which it started. The length of the circumference of the circle is 180 meters. What is the displacement of the car due to its motion? (A) 180 meters, (B) zero, (C) 360 meters, (D) 90 meters.

Here, we’re solving for the displacement of the car that moves around the circle once. We can say that the car starts and stops at this point here in pink. The circumference of the circle is 180 meters. That’s how far the car will travel when it moves around the circle one time. But let’s remember what it means to calculate the displacement of a moving object.

Displacement only has to do with the start and end points of an object’s path. Our car started and ended its journey at this point here. The magnitude of its displacement is the straight-line distance between these points. We see though that the distance between these points is zero; they lie on top of one another. If we were calculating the distance traveled by the car moving around the circle once, that would be 180 meters. But its displacement, because it starts and ends at the same location, is zero.

Let’s look now at another exercise.

Explain why 25 meters is not a displacement.

25 meters is the length of some path that’s traveled. Say, for example, that that path starts here. 25 meters could look like this. But then this path also is 25 meters, so is this one, and so on. We see that 25 meters doesn’t tell us which path we follow, just that it’s 25 meters long. A displacement is different. Every displacement includes a length, like 25 meters, as well as a direction. To identify the displacement of this path, we might say 25 meters to the right, while this displacement would be 25 meters up. By itself, 25 meters doesn’t tell us a direction. For our answer, we’ll write that it is not stated what direction the 25 meters is in. This is why it is not a displacement.

Next, consider this example.

If a distance is traveled in a straight line, which of the following is correct? (A) The distance traveled is the magnitude of the displacement along the straight line. (B) The distance becomes a vector quantity.

To see which answer choice is correct, let’s consider a distance being traveled between this point and this point here. We’re told the distance is traveled in a straight line, so the path will look like this. At the same time, the displacement from our start to end point would be indicated by an arrow like this. We see that the straight-line distance traveled equals the length of this arrow. The arrow shows us the displacement between our start and end points.

Since the straight-line distance between them indicates the length of the arrow, we can say that option (A) is correct. The distance traveled is the magnitude of the displacement along the straight line. The reason choice (B) is not correct is because distance never becomes a vector quantity; it is always a scalar.

Let’s now look at one final example.

A car is at the center of a circle. The arrows show paths that the car could travel to reach the circumference of the circle. Is the displacement of the car between its initial and final positions the same in both cases? Yes or no.

Displacement between two points is the straight-line distance from one point to another in the direction of travel. In our diagram, if we mark out the start and the end of both the blue and the red arrow paths, then we know that the straight-line distance between these pairs of points is the same. They both go from the center of the circle to a point on its circumference. However, displacement includes more than just the straight-line distance between points. It also involves the direction of motion.

If the car followed the blue arrow path to the circumference of the circle, it would move in this direction, while if it followed the red arrow path, its displacement would be in this direction. These directions are not the same, and therefore the displacement of the car is not the same in both cases, either. These two possible displacements have the same magnitude but different directions. We choose answer option (B), no.

Let’s now finish our lesson by reviewing a few key points. In this video, we learned that distance is the length of the path traveled between two points. Displacement, on the other hand, is the straight-line distance between two points in the direction of motion. Distance is a scalar quantity, while displacement is a vector quantity, having both magnitude and direction.

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