Distance and displacement in one dimension

- [Instructor] Previous videos we've talked a little bit about distance traveled versus displacement. What I'm gonna do in this video is discuss it on a one dimensional number line. And we'll get a little bit more mathy in this video. So here is my number line. Let's say that this is a zero, one, two three, four and it keeps going on and then in the negative direction, negative one, negative two, and negative three. And let's say that I start off with a lemon. Let's say my lemon starts off right over here at zero on my number line. And let's say it first moves two to the right so at first moves two to the right. I'll denote that by plus two and then from there, it moves three to the left and then it moves three to the left. And I will use negative for the left. So it moves three to the left. And then let's say that it then moves another one to the left. So then it goes another one to the left and I'll denote negative one as moving one to the left. So based on what we know about distance traveled and displacement, what is the distance traveled for this dot? Distance traveled. Pause the video and see if you can figure that out. Or remember, distance traveled is the entire path length. Or the entire length of the dot's journey. So this is going to be equal to two to the right. So plus two and then three to the left. Now this is an important notion. When we talk about distances, we wouldn't say positive or negative. We just care about the absolute value of the amount that we are traveling. So we won't specify a direction. Now you might say, "hey, "where is the direction being specified?" well implicitly, whether something is positive or negative on this number line is giving a direction. But if we're talking about distances, we wouldn't pay attention to the direction. We only care about the magnitude. So this would be two plus three plus one. Doesn't matter if this is one to the left or one to the right. Doesn't even matter if it's positive one or negative one. We care about its absolute value. We care about its magnitude. So the distance traveled in this example is going to be six units. Whatever the units are on my number line right over here. If these are in meters then this would be six meters. Now what is the displacement? Now remember, displacement is net change in position. Displacement. What is that going to be? Pause the video and see if you can figure it out. Well displacement is going to be you could view this as equal to your final position and we'll use X. Let's say this is the X-axis. So we'll say X final, your final position minus your initial position. It's really just your change in position! So what is your change in position here? Well your final position is you are at negative two at x equals negative two. And then what was your initial position? Your initial position, you started at zero. So negative two minus zero is equal to negative two. So how would we visualize that on our drawing here? Well we started here. Just think about what is your net change in position? You started here. And regardless of what your path was, you ended up two to the left. So your your displacement is negative two. Now displacement, we care not just about the magnitude. We care about the magnitude and the direction. So you might be saying, well, where is the direction specified if I just say negative two? Well, the sign in a one dimensional case is giving us our direction. So the sign is giving us a direction. I started off implicitly with this notion that negative is to the left and positive is to the right. And we're in this one dimensional world. And those are the only two directions that I can travel in. So if I'm in this one dimensional world or if I'm thinking about just one dimension, the sign gives me my direction. So that's why displacement where I care about the magnitude and the direction, I do care about the sign. While distance, where I only care about the magnitude, I don't care about the sign. So I just keep adding up the magnitudes while over here, another way you can think about it, you first get displaced by two to the right so that's plus two. The plus says to the right. Then you get displaced by three to the left. So that is minus three. And then you get displaced by one to the left again. So that's minus one. That's why we're talking about displacement. That's why we care about the sign. And if you are to add all of these together, you are going to get a net displacement of negative two. But an easier way was just what's your final position minus your initial position?