hello welcome back to the physics 1 course the title of this lesson is distance and displacement this lesson really starts to form the actual physics lessons in the physics curriculum that we're studying here the previous lessons were all background material foundational really important material but here's where we actually start looking at some things that are gonna be in every single physics book that you open and that can confuse a lot of people but there's no reason to be confused because every one of these topics is very very simple so we're gonna start with a concept called distance which I think you all know more or less what that means at least in a general sense and also displacement which is a concept that you probably know but you're not maybe not sure what the difference between distance and displacement is so we're gonna talk about that now first before we actually draw anything I want to say that in the beginning of this discussion we're going to talk about 1 dimensional motion 1d motion what does that mean well 1d motion means the motion only can go back and forth along a line so we say this line is the x-direction right so I'm going to draw a picture of a number line but all the tick marks are gonna be X X is equal to 1 2 3 and so on we're not doing any Y Direction motion we're not doing any projectile motion yet we're only moving back and forth along the line of course the we live in three spatial dimensions in the real world where I go back and forth left and right up and down but we're ignoring all the extra dimensions now we're gonna learn what happens we move back and forth along the single line which means and go that way you can also go the other way so in order to represent that we're gonna draw our very important famous number line that we've been using a lot through here why am I doing that because you need to have a reference point whenever you start talking about motion you always have to have a reference point when I tell you I move 13 meters away the first thing you're gonna ask is from where well I might say well I move 13 meters from my house or I might say I moved 14 meters from my front doorstep but if I just come to you and say oh I moved seven meters well that's worthless if you don't know where did I start from I mean you can't be construct my motion unless you know where the starting point is so the starting point here in all of these situations in physics is the origin missed a reference point we call it X is equal to zero this is what we call the reference point also called the origin and of course this is a graph of X which we're gonna say is in meters so the parentheses just mean we're mean we're measuring X but in meters okay so what do we have on this number line we have X is equal to 1 we have X is equal to 2 X is equal to 3 4 5 and so on and they go dot dot you know out forever something gonna take that away and I'll put a 6 right here but they go basically on to positive infinity in this direction as you all know and then they go to negative infinity in the other grade so I'll just take a second and we will mark down some tick marks here so we have tick tick tick tick tick and it goes to negative infinity that way we'll just write it down this negative 1 negative 2 negative 3 negative 4 negative 5 that's enough for right now okay so the question is we're gonna start out with something really really basic right so let's say that you're moving between point number one and point number two or in physics what we say is you're moving from some initial point that's the first point to a final point that's the destination point initial final that's what we talked about in physics so let's say that our initial point is X is equal to 1 right there so we're gonna label it X I for initial that's just where we started from we didn't start at the origin we started one unit away from the origin so if this were my front doorstep then maybe I actually started moving about 1 meter away from my doorstep that's where I started walking from and then my final destination let's say in this example is X is equal to 5 away from the origin so I'm gonna label this guy X some F so you need to kind of get used to the idea in physics of seeing variables like X with little letters or numbers underneath it you're just gonna have to get over the idea I know it looks a little scary at first because you're not used to seeing little little letters underneath the variables but they're gonna be something you're gonna have to deal with all those things mean is they're just telling you something so in this case the eye means that's my initial position this is my final position there so if I want to calculate the distance between here I'm gonna go and write it down this is the initial position and this is the position alright what if I want to calculate the distance traveled so the distance traveled between initial and final how would you find that well you all know that you you ended up at five and you started from one so you probably could all figure out that it's five minus one now I'm gonna put some absolute value signs around this and you'll understand why when I get just a little bit deeper in the examples the distance travel is the absolute value of five minus one it's the same thing as counting one two three four units and five minus one of course you know it's for absolute value of 4 is just 4 so basically we say the distance traveled in this example is true it's trivially easy to see that it's 4 meters 1 2 3 4 right that's what we do we always do subtraction to find distance travel so let's calculate a similar quantity called displacement in fact you're gonna see that it equals the same thing but here's where we start to introduce things that scare a lot of students but there's no reason to be scared displacement is something that we write down as triangle X now the way you write read this in terms of sentence you don't say triangle X the triangle is the Greek letter Delta the Greek capital letter Delta so you read it as Delta X so if I come up to you and I say hey I have a delta X of 2 Delta means change it literally means change and in terms of math and science and physics that's what it means so this quantity means change in and what change in X because that's what follows it change in X okay change in X how do we find change in X well in terms of this thing that we're doing right here it's the final value 5 minus the initial value of 1 pretty much what we did up here but you'll see the difference in a second so 5 minus 1 notice we did not put any absolute value signs there and in fact we're gonna save our our our calculation here in just a second we're going to write it as in general we're gonna say it's the final value of your distance from the origin minus your initial value there so you need to get used to the idea of when you see Delta something Delta anything could be Delta velocity Delta X Delta energy Delta temperature Delta magnetic field Delta electric field whatever whatever it is means change in that quantity and the way you find change is you always take the final value minus the initial value think about if you're taking temperature of water on the stove your initial value of the water when you start might be 75 degrees I'm using Fahrenheit I know that's not great it could be 20 degrees Celsius whatever your initial value of some value of temperature you turn the heat on you walk away you come back and it's boiling okay boiling water is 100 degrees Celsius that's your final value of temperature and if I ask you what's the delta T then you know because I'm teaching you that Delta T Delta temperature means change in temperature and defined change in any quantity take the final value which is 100 minus the initial value whatever it was 20 and then you calculate that difference and that would be delta T now we're just talking about it in terms of displacement so it's a distance Delta X final value minus initial value that's what it is so I'm going to circle this there so in this particular problem what is the displacement in this particular problem Delta X what is it final value is 5 minus initial value of 1 so Delta X is equal to 4 meters okay this is the displacement now you might say well why do I care about calculating this thing called displacement this the same thing as the distance isn't it well in this case yes the first example I gave you they're the same thing distance is equal to displacement but here's the deal displacement is a positive number if the final value is bigger so when you do the subtraction you get a positive value for a displacement in this case like we have for positive value your displacement means you move to the right okay but I can actually have a negative value of displacement if I were to have started here and moved to the left because if I have a delta X and it's always final minus initial if the final value is less meaning this way less than the initial value you'll get a negative number okay so the way to think about this is if you see a displacement of Delta X that's positive it means I moved to the right like this example if I see a Delta X that's negative it means that I've moved to the left because I've actually moved backwards the other way so in physics that is a crucial for you to understand when you deal with displacement or velocity or even delta T like I was talking about temperature or Delta time when you change time anything like that if you get a positive value of Delta whatever it is it means the value has increased in this case we're increasing distance but if you get a negative value of Delta whatever it means that you've decreased the value so the sign is very important for instance later on I'm gonna talk about velocity positive velocity is gonna be positive five meters per second a negative velocity just means like if I have negative two meters per second that just means it's two meters per second but going the other way so the sign tells you which way it's going well it relative to what relative to the origin positive values move this way negative values move this way in this case they were the same because I calculated four meters for the displacement and I take the absolute value of that and I get distance so you might say what's really the distance between or the difference between distance and displacement a displacement can be positive or negative depending on if you're going right or if you're going left distance is I just I don't even care if I'm moving right or left I just want to know how far I moved whether I take three steps this way or if I take three steps this way the distance is the same I just care about how far I moved that's what we typically think of when we talk about distance I don't care if I'm going that way or that way so we throw away the sign to find the distance but the displacement by definition can be positive moving right negative moving left and we have to keep the sign because it's it's useful information which way did I move so let's solidify this stuff by just doing another quick example this will drill it home for you here so let's do another example real quick let's draw another quick little number line like this and we have the origin here I'm gonna do things a little bit faster one two three four five so I'm going to say this is one two three four and five this is negative one negative two negative three negative four negative five we're going to label these negative five negative 4 negative 3 negative 2 negative 1 of course they're zero so then let me label my initial points and my final points let's say you're given a problem where you're told that the initial value of the position is right there at X I'm sorry this is the final value the position and over here is the initial value of the position okay in other words you might think of this as I start out this is my front door I start out four meters away from my front door and then I start walking and I end up two meters away from the front door so I'm kind of walking towards the front door backwards for lack of a better word so calculate the displacement right so the displacement is written as Delta X which means the change in the X variable which is always always always written as the final value minus the initial value this is what you need to remember it's final minus initial and then you just read it right off the chart Delta X is equal to the final value which is a positive 2 minus an initial value which is a positive 4 so now you realize why I spent so much time reviewing things like adding subtracting integers right because now we're taking 2 minus 4 so you're taking a positive and subtracting a number larger and you should know from your rules of algebra that Delta X is gonna be negative 2 units of what units of meters so then you look at this and you say what does this mean well it means the change in X was 2 meters but the negative sign tells me I've moved to the left if it were positive 2 meters and it would have meant I moved to the right but the equation has done the exact same way final value of X minus initial value now let's compare and contrast this to the distance travel the distance travel is just the absolute value of the displacement so I just literally take the sign and throw it away so it's 2 meters this is the final answer by the way I'm gonna circle all my answers with a little bracket that's a habit that I picked up in school so anytime you see this it's not a strange symbol it just means I'm circling instead of a big circle I'm just showing you what the answer is so in a nutshell displacement is how far I moved it also carries Direction information either positive for right-hand movement and negative for left-hand movement distance you don't care about the direction at all all I want to know is how far did I go whether I went that way or that way so I take the sign and I throw it away I only move two meters so if I make sure I have everything in my notes here distance is always positive displacement can be positive or negative depending if you're moving right or left displacement carries more info than distance obviously because you have a sign in there so the numbers are the same but displacement has more information and because it carries Direction info in other words to the right is positive to the left is negative because it carries direction info we're gonna learn in a couple of sections that displacement is actually what we call a vector quantity a vector just to destroy any mystery there's no mystery a vector quantity is just a number or a value that you have that has a a magnitude which means how big is the number in this case it was two but also has some direction information also anything with magnitude and direction is called a vector quantity so displacement is a vector quantity we're going to talk a lot more about it it's not a mystery it's just because displacement is always a number associate and also a sign telling you which way the displacement is going so it's vector this guy distance is not a vector quantity it's not a vector quantity because it does tell you how far you move but it has no information about which direction you move so it's not a vector quantity all right so let's do just a couple more quick examples to solidify things they're just going to take a second then we'll basically be done with this topic problem number three let's say we have a nice number line 0 1 2 3 negative 1 negative 2 negative 3 so negative 3 negative 2 1 1 2 & 3 and let's say you're given is your problem statement you're given that the initial position of your X is negative 2 and your final value of position is 3 and you're told find the displacement find the speed okay well you can plot them on here if you want you don't have to though in fact let's do it without plotting and we'll do it at the end let's go ahead right now Delta X is the displacement okay it's always equal to the final value minus the initial value and we gave you those values right here so the displacement your quantity because it has magnitude and direction final value - but notice you're subtracting a negative number so you need to write it like this you're subtracting it always that's what the formula says but here in place of X I you're actually putting a negative number in place which means what it really is is 3 plus 2 because double negatives make it a positive so what is 3 plus 2 Delta X is equal to 5 meters now what does this tell you it means you moved five meters but it tells you more than that because it's a positive answer it means you move five meters to the right you have Direction information also with the magnitude so if you wanted to plot that or at least verify that it's right go up here the initial value is at negative 2x I final value was at positive 3x F notice that I started here and I did move to the right so I have a positive sign here which means that I also move to the right so everything is reflecting what you see from the diagram how many units to the right 1 2 3 4 5 units to the right positive means you move to the right now if I wanted to write down the distance traveled the distance is the absolute value of the displacement and it's trivial here because when you throw away the sign you get the same thing back so it's 5 meters so in this case just like the first example the distance and the displacement were the same numeric value but this implied positive here actually carries more information because it means I moved to the right tells me which direction I was walking final problem let's go ahead and draw our number line here like this 0 1 2 3 4 5 1 2 3 & 4 5 negative 1 negative 2 negative 3 negative 4 negative 5 3 negative 2 negative 1 okay and then the very first thing I want to do is specify in the problem statement what am I given the initial value of x the start at is at x is equal to 4 the final value of x is going to be x is equal to negative 5 so don't use the number line as a crutch right now let's find the displacement without plotting anything here and just see if the equation predicts reality the displacement is Delta X the change in X it's always the final value of X minus the initial value of X but the final value of X was given in our problem statement it's negative five minus sign comes from here the initial value of X was four now you see why we spend so much time on adding and subtracting numbers right because if you have negative five and you go four more units to the left however you want to think about it all the different review that we did this subtraction comes out to negative 9 negative 9 meters that is the displacement negative 9 meters what does this mean it means that between start and finish I move 9 meters but the negative sign means that wherever I started from I move 9 meters but to the left I kind of walked backwards in the negative direction so that sign here captures that now the distance is just the absolute value of the displacement that we calculated the difference there which is 9 meters because distance is always positive this just tells me how far I went displacement tells me how far I went in which direction now let's see if it makes sense the initial value I said I started at 4 this is the initial value of X the final value is negative 5 way over here let's see initially I started here and I moved to the left backwards so the negative sign means I should have been moving backwards that's totally right how many units we say 9 units 1 2 3 4 5 6 7 8 9 units so this is a good introduction to physics because things like this even though I hope they're simple now for you believe me they trip up a lot of people a lot of people go all the way through the first couple chapters of physics not really knowing what displacement really is and how it differs from distance and so then whenever we calculate speed and velocity in the next section you're gonna be connote you'd be confused because then what's displacement how do I use that to calculate velocity so we're gonna break everything down in this in these classes into step-by-step lessons the main takeaway here displacement is always the final value minus the initial value it can be negative like this one or it can be positive the sign of that quantity tells you have moved right or if you move the left we are getting ahead of ourselves a little bit but we're gonna we know thou the displacement is a vector quantity because it tells us how much and it tells us what rection whereas distance is throwing away the sign information it just tells us how far but it doesn't tell us left or right so there's no direction information for a distance and so distance is not a vector quantity all right make sure you understand this solve them yourself follow me on to the next section we'll talk about speed and velocity and the difference between those two concepts