hey guys hope you're well so this lesson is going to be about displacement time graphs so let's begin so here we have a person that is going for a walk they start at their house okay so that means the starting position is their house so let's just write that over there and then I'm also going to show you on a little number line like this that I showed you in one of our previous lessons when we first started looking at displacement and so this would be the zero position would be their house okay now it says that assume right is positive okay so yeah don't worry about that on the number line but over here that's very important so let's see how this all works now so for the first pot they go from their house and they go up to four meters okay now they said that right is positive so we know that we are going to be over there so that's where the person is relative to their house at this point okay now think about this carefully for this next part which I'm just going to go from here to here you can see that some Learners get very confused with us so if we go here this part is now you back at the house can you see the zero line is the house let's rather highlight that that is the house so what that person has just done there for that red pot is they've actually turned around and they've gone back to their house okay but then they keep walking but now it's going into the negative values so now we're going into the negative values and we're going all the way to negative four so they keep walking keep walking keep walking up to there so this is where the person is now they are four meters to the left of their house so it's they walk this way then they turned around and they walked past their house again and then they walked to the other side okay now if you look at this part over here they're not moving at all why do I say that because if you look the distance from their house the minus four it stays minus four can you see that so for that part over there they are not moving so they're staying exactly over there now we're gonna go on to some questions on this graph and that's how this lesson's gonna go we're going to look at graphs like this and then we're going to answer questions about the graph then we're going to do a question like this and then we're going to answer questions about the graph and then we're going to do this answer questions about the graph you get the idea Okay so we've just done this graph now we're going to answer some questions about it so the first question says what is the total distance walked by this person well we've looked at these before so we know that we've walked four meters over here so that's four meters and then we walked a total of eight meters over here because we went all the way from four to negative four so that's eight meters so it was four meters plus eight meters and that'll be a total of 12 meters the next question says what is the average speed for the full 15 seconds now in previous lessons we've learned that speed is equal to distance over time and we've just seen that the total distance is 12 meters and the total time on our graph is 15 seconds and if you had to calculate that you would end up with 0.8 and the units for Speed will be meters per second this question says describe the location of the person at 10 seconds so at 10 seconds that's when the person um you remember how we drew this that's when the person um finished this part of here okay so the person is currently over here at 10 seconds so what we'll say is that they are four meters to the left of their house because we said right is positive so left is negative so we will say that the person is 4 meters to or let's just say four meters left like that okay that's when they say location that's another word for displacement this next one says describe the location at 15 seconds but what we saw was that between here and here between in that part there they did not move so at 15 seconds they're still going to be 4 meters to the left of their starting position question e what is the person doing between 10 and 15 seconds they are not will give they are not moving and then F determine the velocity between 5 and 10 seconds Ah that's a good question I'll show you why so we know that velocity we've learned this before it's equal to the change in the displacement over the change in time so it's the final displacement minus the initial displacement over the final time minus the initial time but they're only asking between 5 and 10 seconds so they're only talking about that part over there now when we drew this thing over here that was from here all the way up to there that was that part over there right and you might need to just pause and make sure you agree with me on that okay don't just keep going make sure you agree and you say oh yes I do remember we said that so what we can now do is we can look at the velocity as the final displacement now what is the final displacement well that was your final is this part of a year and your initial was this part of it some of you are like yo but Kevin wasn't this the initial wasn't that the start yes but we only talking between 5 and 10 seconds so that becomes your starting position and your ending position okay so the displacement at the final point is -4 so you say minus four minus your displacement at the um at the starting position is positive four right okay so we put a positive four over there and then the time is going to be not 15 seconds you're gonna say your final time minus your initial time and this would eventually give us at the top it'll give you negative eight and at the bottom you would end up with five and so this is going to give us negative 1.6 now remember they said assuming that right is positive but we just got a negative answer so we'll say therefore the velocity is going to be 1.6 meters per second and then we're going to say left because if right is positive then left is negative and we did get a negative answer and so there would be our on server there now with this one I can see on the displacement we're going up to 60 so I just want you to pretend that this is actually 10 20 30 40 50 60 negative 10 negative 20 negative 30 negative 40 negative 50 negative 60. so it is I start riding my bicycle from my house okay so the starting position is going to be the house which is that line over there so that would be the house normally write it over here as well and then we starting over here your teacher's not going to show you this part but I'm just showing it to you because I think it helps you to understand what's happening okay so that's house so let's see what happens here so we're first going to analyze this graph and then we'll go do some questions on that graph so for the first part you can see and it says that assuming that East is positive okay so we can see here that this person starts off and gets to 60 meters okay so they start at the house and they go east is positive so they go 60 meters over there um so that's the first pot so that would be that part there that pot there then for this next part over here they they stay 60 meters that means they're not moving because they're not moving any further away from the house it stays at 60. so we're just going to stay there for the 60 meter pot then for this part here can you see that we are coming back towards the house because this is the house remember and you can see that yeah at this point here the displacement is zero so that means we're not we're not away from the house we at the house so what that would look like is on our graph we came all the way back to the house so that's where we are there then for this part can you see that the displacement is now becoming negative all that that means is we're going in the opposite direction of what we chose as positive so now that is we're going to start going towards the um the West Side okay so for that part we go all the way to 40 but it's 40 on the west side so we're gonna go up to there okay and then over here we're going back to the house again so what that means is we're actually turning around we're turning around and we're going back to the house and so there we are we end the journey back at the house you might need to take 20 minutes if you want to really sit and understand this it's very important that you do understand this so here are the questions are we going to do so it says what is the total distance traveled okay well that's easy we've done that in previous lessons so we know that this first red part was um 60 meters that was this part over here that was 60 meters so we can say um okay for question a we can just say 60 plus then for this green pot there's no distance over there we did not move over there then for this purple part we went back to the house that was another 60 meters that was this part over here so that's 60 meters and then this blue Parts over here um we traveled 40 meters and then this yellow part we traveled back 40 meters again and so 60 plus 60 120 plus 80 is 200 meters that is how far this person traveled to 200 meters next question what is the average speed for the full 55 seconds okay so speed we know speed is equal to the distance over time so we've just calculated the distance in question a so we've got speed is equal to 200 divided by the time which is 55 you see each of these blocks is five seconds so if this is 50 then this is 55. so 55 seconds if we calculate this to two decimal places 3.64 meters per second so 3.64 meters per second question C describe my location when they say describe my location they're just saying your displacement at 30 seconds so at 30 seconds we over there we can see we are all the way back at the house um if I show you on this spot the 30 second Mark was so this first red one was the first 10 seconds then we waited over here for five seconds and then this purple pot is when we came back to the house you see this is when we came back to the house so the location is going to be um zero meters you could even say we back at starting position describe my location at 35 seconds so 35 seconds we are here's 35 seconds okay so that's over here and so if you look on this graph if you read it off it's negative 20. negative 20 that means we are 20 meters so 20 meters west of the house because they said that East is positive so all of these are East okay and then all of these will be West so we are 20 meters to the west of the house it's gonna be over here and then this question determined my velocity between 15 and 40 seconds okay so we know that velocity is equal to um change in displacement over change in time which is the final displacement minus the initial displacement over the final time minus the initial time we obviously know that East is positive okay so it is between 15 and 40 seconds so 15 and 40. so 15 seconds we are over there and then so that's going to be our initial displacement and our initial time and then at 40 seconds we'll be here so that's going to be our final displacement and final time so now we just go fill into the formula so that's going to be uh negative 40. see it's a negative 40. minus our initial displacement is 60 over our final time which is 40 seconds minus our initial time which is 15 seconds and if we had to go calculate all of that we end up with negative 4 okay now if you end up with negative 4 then you need to change your answer to 4 meters per second but now East is positive so then because we got a negative answer we're going to say West like that here's our next example Sarah goes for a walk North is positive okay so that means that all of this is north and then all of this below is south and the starting position would be here so this is start okay so it is that Sarah goes for a walk okay so for the first part can you see that Sarah goes up to two meters okay so Sarah starts over here at the starting position and goes two meters to the north well now we said north is positive and that's why I'm going in that direction over there if she started walking that way then I would have gone that way over there so two meters to the north so we're gonna go like that so that part could be there then you see for this part here Sarah isn't moving at all because have a look here the distance or the displacement is staying at two meters so that's just going to stay over there then for this part up to I don't know like 5.5 seconds or whatever um she comes back to the starting position let's do that in a different color for this part here you can see the displacement is becoming less here it's two here it's one so she's coming back so what that looks like is that okay then for this part she is now going in a South Direction She's going well she's now going to the south of the starting position so she's going one meter to the South so there okay and then over here there's no movement at all so there's no movements over there we can see that the displacements are staying the same so that just stays over there and then this part here you can see she's going back to the starting position back towards the starting position and so that would go like that back to the start right so here's the question so the first one says how far does Sarah walk in total well that's just adding up all these little distances so that would be for this first red part that was two meters so we say two meters plus then over here she did not move then over here that was two meters again you know that's where she came back over here so that's going to be two meters and then for this purple part of here that was one meter you don't look at the direction or the plus and the negatives when you're looking at distance because distance is a scalar and remember when they say how far does someone walk that's just distance that's not just displacement and in this distance of a year was one meter and so two plus two plus one plus one is six meters this next one says describe Sarah's position at seven seconds so seven seconds is over here so you would read it off here so if you had to look on the displacement it's negative one so that means that she is let's say here one meter South because North is positive so then South is negative and we also said that when we drew this graph over here this black line over here was where um she was not moving and it was this Dot and if we read it off there we can also see it's negative one this one says calculate her velocity over the first two seconds okay so the first two seconds is this part over here so we know that velocity is changing the displacement over change in time which is the final displacement minus the initial displacement over final time minus initial time so this part here would be the final displacement as well as final time and then this this part here would be initial time and initial displacement and so that's going to be two take away zero over two take away zero again and that's going to give us one now that must be in meters per second and then we will also say North because North is positive and we just got a positive answer question D says calculator velocity between four and six seconds so that's from here to let's just get rid of all of that up to here so this will be the final displacement final time this will be the initial displacement and initial time so we'll go do that calculation now and so with our calculation we're going to say V is equal to the change in displacement over the change in time and so that's going to be final displacement minus initial displacement over final time minus initial time and so that's going to be negative 1 because that's your final displacement minus 2 over 6 because that's your time minus 4 because that's your initial time and that's going to give us negative 3 at the top and 2 at the bottom and so that's going to be negative 1.5 which is then 1.5 meters per second South South because North is positive so if you're getting a negative answer then that means South and then this last one calculator velocity between 6 and 8 seconds okay so between 6 and 8 seconds we did say that she's not moving so her velocity should be zero but let's go calculated so at six seconds all that lines actually a little bit weird okay but we'll just assume that it's there so that there is going to be your or let's first start at the eight seconds that's going to be your um final that will be your initial that'll be your final time and your initial time so if we had to go do a calculation not with that sorry with velocity we know that that's change in X over change in time and so that's going to be your final displacement minus your initial displacement over your final time minus your initial time and so that's going to be negative one because that's this part then there's a minus and then your initial is also going to be negative one so you're going to put a negative one like that and then your time is going to be eight minus six and so the top part here is going to end up becoming zero so we're going to get 0 over 2 which is zero meters per second and so Sarah is not moving and that's why her velocity is zero meters per second okay let me just put that properly m dot s negative one we've got two more examples well done for making it thus far guys so here we have a question that is Greg is sprinting assume West is positive so that means that West is positive so we know that this line over here is always the starting position and so if West is positive then that would be this part here that's West that's positive and then East is negative and so for that yellow line I'm also just going to fall in that that is the start so let's see what happens so Greg is sprinting wester's positive okay so Greg in the first part goes up to eight meters so that's up to there so that's going to be eight meters like that then for this part over here Greg is not actually going to be moving because you can see that the displacement from his starting position is staying at eight meters so that's just going to be like that over there then for this part from C to D Greg is turning around and going back to the starting position okay so that would look like this turning around going back to the starting position that's at Point D you can actually put the letters d C and then a would be at the starting position so a and then this was also B right so then what happens is that we then start going in an easterly direction to point e which is eight meters um so that would be let me just get a different color so that would go to there so that would be Point e and then and then okay I've got to show the different got to show the color as well so that's from there and then from E to F you can see we're not going to be moving at all because the displacement remains at -8 so that would just stay like that so that would also be letter F and then we've uh this person Greg then turns around and it's quite a funny story Greg sprinting so Greg Sprints One Way quickly turns around Sprints the other way uh pretty random and then let's do this one in yellow so Then Greg goes back towards the starting line so what that would look like is it would go from here um then to the start to the start again so this would be liturgy and there we have it and so now we're going to do some questions on that so it says number one determine the velocity from zero to two so we know that velocity is change in displacement over change in time so that's going to be final displacement minus initial displacement final time minus initial time so it's between zero and two seconds so it's this area here so B will be where we get your final displacement and final time and then initial displacement and also initial time and so that's going to be eight take away zero over two take away zero and so that's going to end up being 4 meters per second and then because it's positive and West is positive we should say West okay so that's for um so let's just say here four meters per second and that is West okay number two says determine the velocity from four to eight so that's going to be from here all the way to here okay so then in that scenario um this part here will be your final displacement and your final time and then this part here will be your initial displacement and your initial time and so if we had to go then use our formula which is change in displacement of a change in time which is final minus initial over final minus initial so that's going to end up being -8 because that's this value over here take away eight divided by time which is eight take away four and that's going to be negative 16 over 4 which is negative 4. so when you get a negative answer all that you then do is you go to the next line and you say four meters per second now because you're getting a negative answer and West is positive then that would mean East so 4 meters per second East so we can say a 4 meters per second East and the last question for this one and then and then we've got one more example after this one okay so determine the velocity from 8 to 10. so from 8 to 10 okay so from 8 to 10 is going to be this part over here so this is where Greg wasn't moving so we should find that the velocity will be zero but let's just see how the calculation works okay so if we just go and use our calculation you would see that this um displacement is negative eight so negative eight minus and in this displacement is also negative eight and then the time is going to be 10 take away 8 and if you have to go calculate this you would end up with zero meters per second and so that is why we say in this area and in this area Greg actually wasn't moving so here's our last example um for this lesson so here we've got we're going up to 40 and down to negative 40. so what I'm going to do is I'm just going to put um make this 10 20 30 40 50 60 and then negative 20 negative 30 negative 40 negative 50 negative 60. okay East is positive so everything above is going to be East everything below is going to be West and then this would be the starting position so we can just say here that that's the start okay so the first thing that this person does is they go 40 East so let's do that in red they go 40 East so that's going to be 2 there then from B to C they are not moving because the displacement remains at 40. so they're just staying 40 the whole time so it stays there and then from what I'm going to do now instead of going from C to D and then to e I'm just going to go straight from C to e because it's one movement you see the line just stays the same okay you can go from C to D and then DT it's the same thing but all that happens is we go from 40 to minus 40. so it's just going to go all the way from here all the way to there but if you wanted to stop at Point D then you would have stopped over there okay but I just want to save a bit of time because we've done this a few times now so we're just going to go to there and then from E you could go to f but because it's one continuous line we can just go straight to G as well so all that it does is it just goes from negative 40 to 20 okay so from negative 40 to 20 positive 20 so it just goes like that and then from 80 to 90 so at that point um or from 80 to 90 we're just staying at the 20 Mark so that means we won't move over there and then from H to I that means we're just going uh back to the start position so I'll just do that in yellow so from H to I we're just going back to the starting position like this okay so with this first question now it says determine the average velocity between 30 and 50 seconds so that's between here and here so we use our velocity equation which is change in X over change in time which is final minus initial over final minus initial and so it'll be a negative 40 because that's um at Point e that's your final position and your final time and then your initial and your initial time and so it's going to be negative 40 minus 40. over the time which is going to be 50 take away 30. and so if we calculate that you're going to end up with a negative 80 at the top and 20 at the bottom and that's going to give us negative 4. so because it's negative 4 then your answer will be positive 4 meters per second and then if East is positive then West is negative and we got a negative answer so we're going to say West okay this next question says determine the velocity for the first 30 seconds okay so it's the velocity for the first 30 seconds okay so if it's the first 30 seconds then this would be your final position and your final time and then this would be initial and initial so if we then go use the formula V is equal to Delta X over delta T it's going to be 40 because that's this displacement minus the initial displacement which would be zero over this time which would be 30. see how it's 30 over there take away zero and that's going to give us one comma three three meters per second so because we're getting a positive answer we could say East so 1.33 meters per second East okay this question says what is the boat doing from G to H so what we said from GTH was that the boat is not moving so not moving and then this one says determine the total distance traveled so the total distance traveled will just be all of these added together so the first part was a 40 meter then this part here we could say was 40 meters or you could just say that this whole pot is 80 meters you know from here all the way to here is going to be 80 meters plus this part is going to be from negative 40 up to positive 20. that's 60 meters so that's 60 meters from negative 40 up to 20 60 meters and then from 20 to zero that's just going to be 20 meters again so 20 meters and so if we're to add this all together that will give us 200 meters