Displacement vs. Distance

by Patrick Ford
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Hey guys. In previous videos, we talked about the difference between vectors and scale er's and we use displacement and distance as examples of vectors and scale er's. We said that there were two similar sounding words to describe how far something moved, and so we're measuring the quantity of length. So in this video, I want to talk about the difference between those and more importantly, to show you how to calculate each one of these things. So let's check it out. Let's actually just take a look at this example Over here. Let's say you had some kind of measuring tape, a ruler, and you went 10 m to the right and 6 m to the left. Well, there's two different numbers that you can get out of these two motions, 10 to the right and six of the left. The basic idea is that the distance, which is represented by the Letter D, is just the total of all the emotions that you dio. It's the total of all the links traveled, whereas the displacement, on the other hand, is a little bit more specific. It's a change in your position in physics. Your position is just where you are on this number line here. It's represented by the letter X, and one way you can think about the displacement is that it's the shortest path between your initial and final positions. Your initial position is just X not. Your final position is X these into the two symbols that you'll see so and this number line here you started off X not, and you ended off at X. And the shortest path is just the arrow that connects those two things. So this right here is your displacement. So let's talk about the numbers in this specific example. So you went 10 to the right and six to the left and the total of all the links that you travel. It's just 10 plus six, and that's 16 m. So notice how this measurement also doesn't have a direction. It's just a magnitude on Lee. So it's a scaler. Whereas the displacement is really just how far you've actually changed from where you started to ending, how far have you actually moved? Well, you went, you went 10 to the right and you went six backwards. So that means you ended up at four. Whereas your initial position was zero. So your displacement is just four minus zero, which is 4 m to the rights. Another way you can think about this also is that you went 10 and then six backwards. So you also get four. Notice how this measurement has a magnitude and a direction, so it's a vector. So now let's talk with the equations. When you're calculating the distance or the total distance, you're just gonna add up all the lengths or all the distances on. There could be many more than two. So, for example, this was D one. This is 10. This was D two, which is six on. Then you ended up with 16 whereas your displacement Delta X, which gets a little arrow on top of it because it's a vector is gonna be your final minus your initial position over here. And that's really all there is to it, guys. So let's go ahead and take a look at some examples down here, we're gonna be calculated the displacement and the total distance from A to B for each of these situations. So we're gonna have X not equals negative two, and then X final equals seven So the shortest path is that arrow that connects them. And so Delta X is just X final minus X initial. So it's just gonna be seven minus negative, too. So be careful with a negative sign. You're gonna add those two things together and we're gonna get plus 9 m to the rights. So for the distance, the total distance traveled, that's gonna be all the distances involved over here, the green multiple. And really, there's just one total distance that you travel. D is just nine you went to and then seven this way, right? So it's to to go to zero and then seven in the posit directions. The whole thing is nine. So that means that your total distance it's just nine. So notice how these two numbers are the same, and that's perfectly fine. They absolutely can be the same number. Let's check out the next example. So now we're actually going to the left in this case, So that's important. We're going from seven all the way to three. So are displacement. Delta X is X final minus X initial. Our X final is three Rx initial is seven and so are displacement. Is negative for meters. So this is also gonna be to the left. So the negative sign or to the left also just means the same thing. Negative signs? Um, yeah, so that just means the same thing. And so your distance over here, your total distance is just again D one d two and so on and so forth. Well, there's only only one distance that we traveled from 7 to 3, but the distance is always gonna be positive. And that's just four. So that means that our total distance is 4 m. Notice how this is positive because the direction doesn't matter, just the total length traveled, whereas this has a negative sign because it has a direction. And so finally, let's take a look at our last example. We're gonna move from four all the way to 10 but then we're actually gonna move back to where we started from. So what is the total displacement? Delta X. It's X final minus X initial. My initial position was actually for I went to 10. But then I went all the way backwards. So that means that I actually ended up right over here. This is my final position at four. So my final minus initials just four minus four, which is just zero. In other words, I haven't displaced anywhere because I went forward and it came back to where I started from. But what about the total distance? Well, this is gonna be D one and d two and so on and so forth. This first distance over here is actually six, because I'm going from 4 to 10. The second one we're going to 10 to 4 is also another six. So this is also six. So let's call that d two it's called is D one and so this is just gonna be d. Total is six plus six is 12. So even though you literally walked 12 m, you've actually displaced nothing because you ended up back to where you started from. So this is the distance, and that's the displacement. So, really, the displacements can sometimes be negative as we've seen before, as we've seen here in these examples. But distances are always going to be positive. And in physics, thes positive and negative signs are usually just used to indicate the direction. For example, we got negative 4 m and that just means that we were going to the left here. We got positive. 9 m. That just means we were moving to the right. That's it for this one. Guys, let me know if you have any questions.