hi this is Mr Anderson and today I'm going to be talking about position versus time graphs uh first thing you should know is that this is part one um I'll also do a part two on position versus time uh part one I'm going to talk about objects that have constant velocity and in the next uh part two we'll talk more about acceleration deceleration and so if you're in the wrong spot make sure you uh start where you should now what do I mean by start uh this whole unit on position versus time graph and and graphing in general is designed so that let me graph out a quick one like that and then let's say it goes like this let's say it goes like this so the whole thing is designed um so that when you are done with this unit on graphing you should be able to take a graph like this and I know that's not super great um but you should be able to take a graph like this a position versus time graph and just looking at it you should be able to figure out exactly what this object is doing uh not only should you be able to figure out what the object's doing you should be able to go from a position versus time graph to a velocity versus time graph and then from a velocity versus time graph to an acceleration versus time graph uh in other other words it's taking me a long time to do this but I can literally draw it so if I say this is the origin so we say this is a velocity of zero I can look at this little unit here and I can figure out that it's going to have a velocity of like that uh and then it's going to have a velocity of like that and then the velocity is going to go like that and if and if you don't know how to do that like that um um then you're in the right spot because we're going to start right here if you do know how to do that and then to go from here to an acceleration graph then don't watch these videos because you clearly know what's going on so let me clear that off I'm sorry I got a little into that uh and let's get started uh best place to start is with the moving man now what is the moving man moving man is a simulation that was created at uh University of Colorado and what they do is they move a man about and you can actually start to play around with position versus time graph and so if you're struggling with this please go there and even if you're not please go there and that's what we're going to do as well so here's the moving man and if I hit play at the bottom now I've paired it down so I really only have the simplest things you also could have velocity and acceleration but since this is position versus time I'm just going to um start there and so I've hit play and what we can see is that our man is not moving and so our graph keeps him right at zero okay so that's kind of Bor boring so let me clear that again and let's play it again so what you can do is I can input the man's position so I'm going to move the man to five and what you see is the man up here quickly moves to position five and you can see that reflected in the graph down here so let's move him to neg five or let's move him to eight or let's move him to six or let's move him to8 okay so if I pause it right here let's look and you can hit playback and then we could watch what happened and so for this first period of time he was at position zero and then it quickly moves to position five and so what a position versus time graph really tells us is where he is or she is he then quickly moves back into the negative and then back into the positive and then a little less positive and then finally moves into the negative again and so if you see a position graph like this position is always going to be graphed on the uh y AIS and time is always going to be graphed on the x-axis if you see a graph like this it simply is a man position positioning himself in different positions um now it's a little unrealistic in other words we cannot move that quickly and so let me move him back to position zero and show you what it might look a little bit more like um so let me play it again and what I'm going to do is use this dragger to actually move him in a natural fashion so let me try to move him in a natural fashion to position five and then let him rest there for a little bit now let's M move him back maybe to position one and then way down here very quickly into it looks like position four and a half and then let's have him rapidly go up here at the end okay now let's watch that cuz I was controlling it so it was hard for me to watch let's watch what happens so there's a long period of time when the man is not moving but then the man moved from position zero to position five and so that is should be a straight line when I was trying to do it and so what that straight line indicates let's try and go back and see if we can see that again let's watch his behavior as he goes it's a little jerky but you can see that the man is moving and since this is a straight line the man should be moving at a constant velocity or in other words he's not accelerating let what happens watch again okay now the man moves back so the man moves back to this position like position one and the speed here let's go look at that so the speed of the man's movement right here watch how fast he's moving and the speed of the man's movement over here let's go way back here again is constant and so what does this mean when the line is moving up it just means that the man is moving to the right and what does it mean when the line is moving down it means the man is moving to the left now this line looks a little bit steeper so the Lots Watch What Happens can you see how the man's moving faster and now let's watch the man at the end the man whoa really moved and so the the slope of this line also tells us the speed and so that's the first rule uh first rule that you should pick up at least that I've picked up is that the slope slope equals the velocity and if there's no slope so if slope equals zero um then the man's not moving at all so here um if the slope is negative then the velocity is negative and it doesn't mean that it's somehow going slower it just means that it's moving in the opposite direction so it's moving down like that and so that's what you can learn from moving man you can move it back and forth and you can try to figure out what position versus time graph is now on our test we don't have to play with the moving man on our test we have to solve problems and so let's get to some actual problems so what do we have here now we're not given the man but we're given the position versus time graph and so knowing what you now know what does this mean well first of all it's a slope slope it's a positive slope and that means the man is moving where's the Man start at position zero and time zero and where's the man end at position um six and at time three so what did the man do from here to here the man walked and walked with a constant velocity now the cool thing is that we can actually use the slope of this line to figure out how fast uh the man is walking so what's the rise in this well it goes from 0 to six and so the rise is is going to be 6 M what's the run it goes from 0 to 3 and so that's going to be 3 seconds and so the Velocity in this case is actually 6 m per 3 seconds or 2 m/ second um now we learned in the last podcast that velocity is position final minus position initial over time final minus time initial and that's all we're doing in slope in other words the slope of this line is giving me the velocity of that object um so to solve that in a in a more roundabout way let's kind of go down to this next one so let's go right here and figure out the velocity of the man here well if we look down here the final position is 3 m the initial position is 6 M um the final time time is 8 seconds right here and the initial time is 5 Seconds and so this should be -3 M divided by well 8 - 5 is 3 seconds and so during this period of time the speed of the man or velocity is -1 m/ second and so our speed here was 2 m/s our heat our speed here is zero because the man's not moving again and then down here it's -1 m/ second and then finally it's zero again and so if we clear this off again a goal was to be able to graph that so I'm going to graph this as put this as zero velocity right across the middle and so from position one to position three so position one to position three what was the velocity the velocity was was and let's make this one and make that two on our scale so from here to three the velocity was actually 2 m/s it's going to be a straight line now what was the velocity from this period so from period 3 to period 5 so time 3 to time five was actually zero so I'm going to draw a straight line right across here and then you can connect that with a vertical line like that should be straight vertical okay so the velocity was 2 m then it was 0 m/ second second what was it during this period of time we just calculated it for the next 3 seconds 1 2 3 it was -1 m/ second so 1 2 3 it was - 1 so we'll call this negative 1 right here and this would be one and then what was it at the end at the end it was Zero again and so this would be the velocity versus time graph for that object it was going a constant speed in the positive in other words he the moving man was moving to the right he then paused for a little bit of time he then went in the opposite direction not as fast you can see that the slope of the line is not as steep as it was over here and then the man waited for a period of time and so that's how you'd go from a position versus time graph to a velocity versus time graph and the easy way to do that position versus time to Velocity versus time is just to figure out the slope CU if you figure out the slope of the position versus time graph that'll always tell you the the uh the velocity versus time graph if that doesn't make sense go play uh pH it's P.C colorado.edu play with the missing man or the moving man and then take a stab now if you play around a little bit what you're going to find is that it's not always as straight in other words when we were doing it moving man was moving straight to here and then resting and straight to here and resting but in this graph you see that it's actually a curving line on the velocity and what that means is or on the position versus time and that means that its uh velocity is changing um so you could try to figure out what the velocity versus time graph is or you could watch position versus time part two and I'll give you some tips uh so I hope that's helpful