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previous videos we've talked a little bit about distance traveled versus displacement what I want to 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 0 1 2 3 4 and it keeps going on and then in the negative Direction negative 1 negative 2 and negative 3 and let's say that I start off with a lemon let's say my lemon starts off right over here at 0 on my number line and let's say it first moves to to the right so it first moves to to the right I'll denote that by +2 and then from there it moves 3 to the left then it moves 3 to the left and I will use negative for the left so it moves 3 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 1 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 well remember distance traveled is the entire path length or the entire length of the dots journey so this is going to be equal to 2 to the right so plus 2 and then 3 to the left now this is an important notion when we talk about distances we want 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's the direction being specified well implicitly whether something is positive or negative on this number of 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 matter if it's positive 1 or negative 1 we care about its absolute value we care about its magnitude so the distance traveled in this example is going to be 6 units whatever the units are on my number line right over here these are in meters and this would be 6 meters now what is the displacement and remember displacement is net change in position this place mint 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 2 at x equals negative 2 and then what was your initial position your initial position you started at 0 so negative 2 minus 0 is equal to negative 2 so how would we visualize that on our draw 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 and now so you might be saying well where is the direction specified if I just say negative 2 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 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 could think about it you first get displaced by two to the right so that's plus to 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 we're talking about displacement that's why we care about the sign and if you were 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

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