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### Course: Mechanics (Essentials) - Class 11th>Unit 4

Lesson 1: How far do we really go at the end of the day? Exploring the difference between distance and displacement.

# Distance and displacement introduction

An introduction to the difference between distance traveled and displacement. Created by Sal Khan.

## Want to join the conversation?

• If it didn't go 10 km west, you would use the Pythagorean theorem, right
• Everyone else on Pythagorean's Theorem: Yes, it makes sense!

Me: Why are we still here, just to suffer...
• Would it be correct to say that displacement is the end-point, the last stop?
• Not exactly. Displacement is the shortest distance from your initial position to your final position. Therefore, displacement is a measurement of distance and not an "end-point."
• i did not understand the exact meaning of displacement?
• Displacement is the final distance of a point from the initial point.
For instance, if I walked 10 meters from my house, then walked 5 meters towards my house, my displacement from my house would have been 5 meters, even though I walked 15 meters in total.
Displacement is more of an a-to-b measure, rather than a how-did-a-get-to-b measure, if that makes more sense.
• If the sheep traveled 10km east, 5km south, 10km west, and then 5km north will the displacement be 0?
• Yes, because the sheep will walk in a square, therefore, the starting position and ending position will be the same, so the displacement is zero because 0-0=0
• Why would it not be correct to say that the sheep travelled -5 km south?
• What you are doing by saying -5 km south is giving the direction twice: the first time by denoting the "-" symbol before the five and a second time by saying "south." You want to use only one method of indicating direction.
This can be done by using a positive/negative symbol or by using a direction word such as north, up, down, west etc.
• From we can say that the * definition of displacement is "change in position" * and for * distance is "total length of path travelled" * ?
• Well yes we can that displacement refers to the change between the initial and final position and distance refers to the whole length of path covered by an object
• Did the sheep get its food at the end?
• hopefully it did.
• What will happen if it moved 8 Km west instead? how would you find that?
• If you mean that after moving five kilometers to the south, then move eight kilometers to the west, you can find it by using the Pythagorean law and trigonometry.
• This might not be totally on topic, but...
I've noticed some people here in the comments mentioning the Pythagorean Theorem as a reference to the problems in this lesson. While I am familiar with the theorem itself, I have no idea how that would apply here.
Could somebody explain how you use the Pythagorean Theorem in physics?
Sorry if this is a silly question-this is my first time studying physics (and I'm lousy at math) :)
• You can use the pythagorean theorem to find the distance between any two points on a coordinate plane as part of the distance formula. People are just mentioning that if the sheep hadn't gone West you would've needed to use the distance formula to figure out the displacement of the sheep because it wouldn't have been immediately obvious.
• since when did the cursor get so huge
• sal's cursor?

## Video transcript

- [Instructor] So let's say we have a sheep and it is hungry. So that is my sheep. My best, quick drawing of a sheep and it is just following the grass wherever it finds good grass to eat and so in pursuit of tasty grass, it first goes 10 kilometers to the east, 10 kilometers east and then it takes a right turn and then it goes five kilometers south, five kilometers south and then it takes another right turn and it goes 10 kilometers west, 10 kilometers west. My question to you is how far has this sheep traveled? And pause the video and see if you can figure that out. How far has that sheep traveled? Alright, now let's try to answer this together and it's a little bit of a trick question because depending how you interpret the idea how far something has traveled, there could actually be two valid answers here. One answer is you could say what is the total distance traveled? So let me write this one down. This is an important concept. Distance traveled and this would be the total length of its journey or the total length of its path. So the distance traveled in this situation would be 10 kilometers plus five kilometers, plus five kilometers plus 10 kilometers, plus 10 kilometers which would give us 25 kilometers. That would be 25 kilometers. So some of you all might have said that the sheep traveled 25 kilometers. If that's what you came up with, what you calculated is the total distance traveled. Now, some of you might have said, wait, hold on a second, the sheep was here before and then it ends up right over here at the end of its journey and so its change in position is it would have moved a net five kilometers south. From this point to this point would have been five kilometers south. It doesn't matter what it did along the way, what its path was. At the end of the day, it ended up five kilometers south of where it started out and this would also be a valid way of saying how far it traveled and this notion is known as displacement. So the displacement would be in this situation five kilometers south. So pause this video. What do you think is the definition or the difference between saying the distance something traveled versus its displacement? Well, as we mentioned, the distance something travels is the entire length of its journey. It's the entire path and this thing will never be negative. You could travel zero kilometers but as long as you are, your position keeps changing, this thing will only increase because it's the total length of your path. Your displacement is your change in position and since it's a change in position, not only will we mention the five kilometers, we'll say in what direction. The position of the sheep has changed five kilometers to the south. So let me write this down. This is total length of path, total length of path is the distance traveled while the displacement is the change in position, change in position.