hey guys hope you're well so in the previous lesson we started looking at a displacement time graphs in this lesson we will be focusing on velocity time graphs now we're going to take a little bit of time trying to understand what the graphs represent remember that this is not a displacement time graph this is now a velocity time graph so it has its own uh understanding and it's a totally different kind of graph okay so let's have a look if we for example look at this position over here okay over there um wait why is it doing that there section over there is probably one second somewhere around one second and if you look at the velocity it's one now the velocity is positive one so it says that East is positive so that means that at this position over here the person let's just say here uh person is walking at 1 meter per second remember meters per second is almost like a speed velocity is almost you can think of it as almost the same as speed yes they are a little bit different as we've learned already but you can think about it as how fast is the person walking so the person is walking at one meter per second over there and they're going in an easterly Direction why because the velocity is positive and East is positive okay now if you for example look at this position over here let's say the time is I don't know four seconds maybe and if you look at the velocity the velocity of that person is three so it means that along this line the person is walking faster and faster and faster so we can say that the person is accelerating because when an object is getting faster and faster and faster and it's not just moving at the same constant speed or velocity but it's getting the velocity is changing then it's accelerating so here we're at this position over here we could say that the um we could say that actually let's make this a lot neater I'm not making this really neat let's say that this is position um this will be position a let's say this is position B and let's say position C and let's say e let's go for the up till there for now so a b c d and e so what we said at a was that they are um moving let's not say walking oh no they are saying they're walking okay so walking at one meter per second East okay now at point B we said that the velocity is three so they're still walking East uh three meters per second so they're still walking East so they have not changed Direction okay now at Point C they are now walking at four meters per second so walking at four meters per second East now here's where Learners start getting confused they think that when it goes down like this the person is start is turning around that is not true that is only true when you are looking at a displacement graph on a displacement graph um then when you start coming down like this then it means the person is coming back to the starting position which we used to label like this but that only works on a displacement graph check this out if you were to look at Point e let's actually put Point e over there now if you had to read off the E values velocity look at that it's still the person is still walking now they're walking at two meters per second but they still going east ah they have not turned around if they turned around they would be going west they are still going east okay so the velocity is they just all that's happened guys is here on this part the person was getting faster and faster and faster and now they have not turned around they're just slowing down a little bit but they still going east okay now if you look at this point of a year which we'll call if we can read off the velocity is zero so all that the person has done there um oh sorry that was meant to say d i see where there's a confusion that was meant to say d and now um oh I see okay there we go and now e okay oh no f ah let's call it e over there my goodness sorry guys so e the person has stopped person is let's say their standing still person is standing stop okay but they have not turned around they didn't turn around for any of us okay they just they walked in One Direction they were always going east and now they've just stopped and they're just chilling for a bit okay now if for example we look at Point F now if you look at Point F the velocity is negative three okay so what that means is that the person is walking at three meters per second but now they are walking in a because the velocity is negative they're going west because of Easter's positive West is negative okay now if you look at Point G and then we're also going to look at Point H so at Point G the person is now walking at negative four uh oh what do you write in there person is person is walking 4 meters per second so the thing I'm trying to make you understand is that this is a totally different graph to displacement and you must not think of them as the same thing it's totally different okay so the person is walking four meters per second um what did we say West now on a displacement graph on a displacement graph that we looked at in the previous lesson when this line became flat then we would say that the person is not moving but that is not the same on a velocity graph how is it not the same well look at Point H if you look at Point H what is the velocity ah the velocity is still um the person is still walking at 4 meters per second so the person is they can't be standing still they're walking uh four meters per second and they're still going west so can you see that when the graph is going like this the person is getting faster and faster and faster so in that yellow part we can say person is walking faster we can say the accelerating that's a better word we can say a person is accelerating because they're getting faster and faster now over this area over here the person was slowing down remember we said that the the velocity was getting less because at a from yeah you you understand what I mean right I wish we spoke about that for example over here the velocity is three but then over here the velocity is one so the person is getting slower so for that green pot we can say person now they're slowing down so I'm going to use the word decelerating remember I spoke about in one of our previous lessons about positive acceleration negative acceleration and how a lot of teachers get that part wrong okay if someone's speeding up they're getting faster um we accelerate getting faster and then if someone is getting slower you can call that deceleration so getting slower or let's say slowing down slowing down now in this area over here some Learners say that the person is getting slower but that's not true if you look at the numbers don't worry about the negatives just look at the numbers it's going from one so for example there the velocity is one but then there the velocity is two there the velocity is three and they're the velocity is four so for that part there the person is actually accelerating the negatives just telling us that they're going in a Westerly Direction that's all that that means so they're not getting slower there so for that blue pot we will say that the person is accelerating and what I could have even said over here was East over here I could have said East for this one let's rather write it over there and then for this one the person is now going in a West Direction and in this last little piece we can say person is moving at constant velocity so a person moving at constant oh and for the rest of this lesson by the way we're still going to do calculations you see we're going to do calculations I'm even going to be showing you like how to calculate the area under the graph maybe your teacher showed you something like that we're also going to be calculating yeah all sorts of stuff and we've got quite a lot of examples coming up okay so stick around we're just getting into the introduction still so a person moving um at a constant velocity so when you're moving at a constant velocity we can say that the acceleration is zero acceleration is equal to zero and we are moving in a Westerly Direction Why do I say West well if you look at the velocity the velocity is negative four so we know that East is positive so then West is negative okay now let's go and actually analyze this question uh well let's go look at the questions and do some calculations now we're going to start looking at all the questions and there's some really interesting things we're going to learn uh we're going to start looking at the area under the graph and we're going to learn what that means so yeah the first question says determine the acceleration Okay so we've learned that acceleration is equal to the change in velocity over change in time and when we expand that formula It's the final velocity minus the initial velocity over the final time minus the initial time now when they say final and initial I don't want you to just think start and finish no it depends on where they are talking about so they say determine the acceleration in the first five seconds okay so that would be from here up to here so up to five seconds so it's this part of the graph because that's five seconds and the spot so this part over here would be the final and this part would be your initial remember final means the last part and the initial means the start part of where they are talking about okay and then this would obviously go with the final time and then this would go with the initial time so if we then go use our formula the final velocity is four then the formula says there's a minus and then what's the initial velocity zero What's the final time five seconds and what's the initial time zero seconds if you work this out you get zero comma eight now the units of acceleration is m dot s minus two and now have a look at this positive we got a positive answer so the answer is e so we can just say here 0.8 meters per second to the negative two ah things are going to start getting interesting what is the total displacement for the 15 seconds I want you to write this down somewhere or you need to memorize this but displacement or whenever they talk about displacement or when they talk about distance on on these types of velocity velocity time graphs I want you to think of area okay I want you to think of area so the way that it will work is the following now I'm going to do a lot of examples with you in this lesson so just bear with me it might be a bit weird for this first calculation that we do okay but just trust me it's gonna get it easier so have a look here it is what is the total displacement so I want you to think of area for the 15 seconds so what you do is you're literally just gonna go look at the area under the graph so you're going to go calculate this entire area over here okay so you're going to calculate that area oh and I forgot to mention before we started this question this time of year we're going to assume that that's 7.5 in a test they'll make that a lot clearer and then okay so you're going to find that area over there and then you're going to have to go find this area over here up to there so it's it's the area um between the x-axis and the curve can you see that so here's the x-axis okay and so so that's the x-axis and then the curve so you let me show you once again so you see you've got the x-axis and then you're just going to fill in the the the the space all of that and then here you've got the x-axis and then you're going to fill in the space up to the 15 seconds which is where we stop okay now what you are going to go and do is for the displacement or let me first show you something um sorry sometimes while I'm thinking about the best way to explain it I think of a new way to do it so what we're going to do is we're going to go work out the areas okay so we're going to go work out the area of the shape over here and then we're going to go work out the area of the shape over here now this shape is a triangle now to work out the shape of a the area of a triangle you could do this in two different ways you could either draw a perpendicular height over there and then you could work out the area of this one and then you could work out the area of that one and then just add them together but there's a better way did you know that the area of a triangle is half base times perpendicular height we have if you look at the base it's this entire piece of ear that would be 7.5 that's how long that would be 7.5 and the perpendicular height we actually know the perpendicular height it is from the top here to the bottom and that height would be four okay so you could just go work out the area of this triangle in one step but if you're not comfortable with that as I said you could work out the area of this side and this one and then just add the two answers together so for that one you're going to get half base another base is 7.5 and the height is four okay so that's the first part let's call that section A so we've done section A and if we calculate that we get 15 okay now that's just gonna be 15 meters I know that area is meters squared but if you but what I told you is that area to find the displacement um we just need to find the area under the graph and displacement is measured in meters okay now we're going to go find the area of this piece now you could get fancy if you wanted to and you could be like oh yo bro this is a trapezium but for the most students I think we'll all just be more comfortable let's break it up into a triangle let's break it up into a triangle which I'll call section B and then we can do this rectangular um kind of shape which we'll call C so for B it's a triangle so half base times height so the base would be from here to here so what is 7.5 up to 10 well that's 2.5 right so this length is 2.5 so we say 2.5 now here's where you got to be um here's where you got to be quite careful so look at the height it goes from zero to negative four so that height I want us to put that height as negative four okay because yeah you'll see why we do that now so you're just going to put that as negative four and if you had to go calculate that you get negative 5 meters okay and then we're going to go work out the area of section c and so that's going to be a rectangle which is just length multiplied by breadth so that's going to be the length as five and then the the height or the whatever you want to call it is going to be negative four and so that's going to give us negative 20. now here's the important part okay uh when you are calculating distance when you're calculating distance which we are going to do in question C you just add the numbers together but without the negatives so you just say 15 plus 5 plus 20. you don't look at the direction or the sign you're just looking at the the actual value and so if you had to go add that up you're going to get 40 meters okay that's for uh distance 40 meters when you are doing displacement remember that displacement is a vector so it has direction as well so all of these positive numbers are East because East is positive and all of the negative ones whoopsie all of the negative ones are going to be considered um West because we said in the previous slide that at this part over here the vehicle was moving West okay so it makes sense that the displacement is negative and so for displacement you are going to take all of these signs into account so you're going to say 15 minus five well you could plus them you could technically say plus and then that one's negative five and then plus negative 20. and if you had to go work this out you would end up getting a negative 10. so what that means is that the final displacement is going to be 10 meters West because East is positive West would then be negative so for distance you just add all the numbers together for displacement you take the sign into account okay so let's go do a whole bunch more practice now let me just quickly fill this in 10 meters West notice that I have to give the direction because y displacement is a vector for distance you don't because it's just a scalar let's go practice this some more I know it might be feeling a bit weird still okay let's have a look at this one I start riding my bicycle from my house assume that East is positive okay so if we look at this first section over here this first section I'm going to call the section A or actually let's stick to what we did earlier so we're going to do that so that first part if you look at what happens as I start riding my bicycle from the from resting position at zero and then I increase my speed all the way to 60 meters per second geez that's actually really fast that's like uh what is that that's if we convert that into kilometers per hour wow I'm riding my bicycle at 216 kilometers per hour maybe it's a motorbike okay so we increasing we're going all the way from zero up to 60 meters per second so you see how we are accelerating over here we're getting faster and faster and because the velocity values are positive it means we're moving in a easterly direction okay so for that yellow part we are accelerating and we are moving East okay now for this part over here some Learners will say that we are not moving but that is because they are confusing this graph which is a velocity graph they're confusing that with a displacement graph which we've looked at in previous lessons you cannot you're not you're not standing still over here you're moving look at this your velocity is 60. so you are moving you're just moving at a constant velocity you're not increasing or decreasing your velocity it's staying the same so this part which I'm gonna put over here is going to be moving at a constant velocity moving at constant velocity and because the velocity is positive we're still moving East okay and then we'll say that there is no acceleration or we'll say that the acceleration is zero there's only acceleration or deceleration when your speed is or your velocity is going up or down but when your velocity is staying the same you're just cruising along at 60 kilometers or 60 meters per second okay now for this part here some Learners will say that we are turning around but that is because they are thinking of a displacement graph if it was a displacement graph then you have turned around but on a velocity graph think about this carefully if you look at the velocity over here look at the velocity over here the velocity is 40 and it's positive so you're still going east you look at the velocity here it's 20 and it's positive so you're still going east so all that happens from here to here is the person maybe started using their brakes and they're just slowing down but they still moving East they still moving away from the starting position okay but if it was a displacement graph then this would mean the person has turned around but this is not a displacement graph this is a velocity graph so all that's happening is the person is just slowing down think about yourself riding a bicycle if you start pulling your brakes you're still gonna go in the same direction but you're just slowing down so for that part we could say um we are decelerating now because our speed is slowing down while velocity we're decelerating but we're still moving East we are still moving East now at this point over here if you look at your velocity well okay if you can't highlighter red zero with the red highlighter if you look at this part here our velocity is zero zero so that means the person is standing still so person is not moving okay now if you look at this part here now some people would say that the person is slowing down because as soon as they see this they see slowing down now this part was slowing down you see this is where you've got to understand these things so carefully so here we were slowing down because look at this your velocity went from 60 to 40 to 20. so you are slowing down but if you look at this blue pot you're actually speeding up because look at your velocity over here it's 20 and then look at your velocity over here it's 40. the negative just means that you're going in the opposite direction but you're actually speeding up so even though this line and this line looks the same when it was here you were slowing down and when it was here you're speeding up you just have to look at the value on the y-axis over here you're going 20 and over here you're going 40 so you're speeding up the negative as I said just means that you're going in a Westerly Direction that's all so when the person got to here they stopped turned around and now they are going in a Westerly Direction okay so we can say here that they are accelerating um and they are moving West because the velocity values are negative okay now for this last piece you might be tempted to say oh the person's speeding up because when we look when we had a graph look like that earlier that means speeding up but it's not true you have to look at based on where we are on the graph so if you look at this the velocity um over here over this this part the velocity was 40. I'm not going to worry about the negative that just means the direction so the 40 Okay then if you look at the velocity over here if you read it over there it's like negative 10. well just pause it you can think of just 10. so the person from here to here is slowing down foreign and when they get to this position the velocity is zero so here they have stopped again so from here to here the person is using their brakes and they slowing down so um we can say that we are decelerating because we're slowing down and we're moving West why are we moving West well if you look at all the velocity values they're negative and East is positive so West is negative so decelerating and moving uh West so it's really important that you understand exactly how we got each of these things okay now we're going to go do some questions on this so the first question says determine the acceleration in the first 10 seconds so we know that acceleration is equal to change in velocity over change in time which is then final velocity minus initial velocity over final time minus initial time so they're only asking for the first 10 seconds they're not asking for all of it so the first 10 seconds is up to there so that means over here and over here so this would be your final velocity as well as your final time and then this would be your initial velocity and your initial time and so if we had to go fill this all in your final velocity is 60 minus your initial velocity is zero your final time is 10 seconds and your initial time is zero so if you had to go work this out you get six and then that's meters per second to the negative 2 and then because it's a positive answer East is positive so we must say East so we're going to say 6 meters per second East or six six meters per second to the negative two okay that's important next question B says determine the total distance traveled so remember what I've told you in the previous um in the previous slides is that when you have a velocity graph only when you have a velocity graph then distance whenever they say distance or displacement I want you to think about area under the graph now when we talk about area under the graph I just want you to look at the x-axis which is this one and then you're just going to fall in the Gap so there and there okay now let's go work out the area of those sections so this part here you could be fancy like and do a trapezium but I think what most Learners would like to do is a rectangle well okay that's not a rectangle it's a triangle my dude so a triangle over here which I'll call A then a little rectangle over there which I'll call B and then a triangle over here which I will call C and then a this is one big triangle so we could just do that as one big triangle if you wanted to you could do two smaller triangles but it is just one triangle so it's going to go D okay so so for section A it's a it's a triangle so we're going to go half base times height so the base length would be from here to here which is 10 seconds and then the height is see now the height of the triangle is going to be that part and so that's going to be 60. so we're going to put 60 over there if we had to go work this out we end up with 300 now remember we're working our distance and displacement so that's meters for Section B that's a rectangle so for that you need the you know with a rectangle you multiply this side with that side and so we're going to take for example this length which is five because it goes from 10 over here and then this one in the middle would be 15 so that's 10 to 15 that's only five so we're going to say five we don't say half half is only when it's a triangle and then the height is going to be 60. okay so we're going to say 5 times 60 and so that's going to be uh 300. meters now we're going to do section c which is a triangle again so that's half base times height so the base length would be this part of a year so that goes all the way from 15 which is this part from 15 up to 30. so that's going to have a length of 15 because 15 to 30 is 15 and then the height of that triangle is all the way up to there so that's going to be 60 again so 60 and so this gives us 450 meters all right so now we just need to do this part and so this one is also a triangle so it's going to be half base times height now the base goes from here up to here and so that is from 30 all the way to 55. so what is 30 up to 55 that's 25 okay now for the height the height of that triangle is from here to here you see it's that height over there so you've got to look on the y-axis of the n and you can see that it's going from zero up to negative 40. so that height is negative 40. so we include the negative okay and if you had to work this out you're going to end up with you get Negative 500 meters okay so now when we calculate distance when we calculate distance we just add the numbers together and we don't worry about the negatives so for question B when you calculate the distance you're just going to go 300 plus 300 plus 450 so we'll just say plus 500 over here and if you had to go calculate all of this you end up with 1550 meters now when you look at displacement you do take the sign into account so you're going to say so for question C you're going to say 300 plus 300 plus 450 plus and then this is negative 500 and so if you had to go calculate that you get 550 meters but now you're getting a positive answer and East is positive so we say East remember displacement is a vector so it needs Direction so we're going to say 550 meters East I'm just going to put an e there for East okay this one says determine the acceleration okay so we know acceleration is change in velocity over change in time which is then final velocity minus initial velocity over final time minus initial time but but they're asking us to only look between 40 and 55 seconds so 40 and 55 seconds that's from here and then 55 seconds is here okay so these are the two positions that they're asking us now which one is later or which one is the final one this is your final one because it comes at 55 seconds so this is your the one to the right is your final so this is your final and this will be your final time and then this will be your initial and your initial time Kevin I thought this is the initial velocity no it depends on where they are talking about so if the question is talking about the spot then this is your final this is your initial if they were talking about from here to here then this is your final this is your initial okay so let's go fill in our formula now so the final velocity is zero if you read off the velocity there your initial velocity is over here but remember that you mustn't look at that 40 that's the time you've got to look on the velocity axis and so that's negative 40. you see there it's in line with that so it's negative 40. so you're going to put negative 40 yes you see you have two negatives next to each other there and then for your time your final time is this one which is 55 seconds and then your initial time is this one which is 40 seconds minus 40. and so if you had to go calculate that you end up with 2.67 and that's meters per second to the negative 2 because that's what acceleration is measured in now we just got a positive answer so because East is positive we're gonna say East but Kevin how can the exhilaration be positive if the velocities are negative guys acceleration velocities are slightly different things these are the velocity values so the velocities are negative here but it doesn't mean your acceleration is going to be negative so that's going to be the end of this lesson but if you still want to practice uh some more of these then I'm going to add another video so just look for the video immediately after this one where we can or where you can do some more practice questions okay