Friday, May 20, 2022

Position vs. Time Graph – Part 1

Hi this is mr. Andersen and today I'm going to be talking about position versus time graphs first thing you should know is that this is I'll also do a part two on position versus time part one I'm going to talk about objects that have constant velocity and in the next part two we'll talk more about acceleration deceleration and so if .

You're in the wrong spot make sure you start where you should now what do I mean by start this whole unit on position versus time graph and graphing in general is designed so that let me graph out a quick one and then let's say it goes like this let's say it goes like this so the whole thing is designed 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 on 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 not only should you be able to figure out what the objects 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 in 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 and then it's going to have a velocity of like that and then the velocity is going to go that and if and if you don't know how to do that like that 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 unless get started best place to start is with the movie man now what is the movie man movie man is a simulation that was created at University of Colorado and what they do .

Is they move a man about and you can actually start to play around with the 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 as well so here's the movie man and if I hit play at the bottom now I've pared it down so I really only have the simplest .

Things you also could add velocity and acceleration but since this is position versus time I'm just going to 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 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 negative five or let's move him to eight or let's move him to six let's move him to negative eight 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 X graphed on the y axis and time is always going to be graphs on the taxes if you see a graph like this it simply is a man position positioning himself in different positions 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 might look a little bit more like 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 Mizzou move him back maybe to position one and then wait and here very quickly into 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 because 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 that's 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 of watch .

What happens can you see how the man's moving faster and now let's watch the man at the and demand whoa really moved and so the the slope of this line also tells us the speed and so that's the first rule first rule that you should pick up at least that I picked up is that the slope slope equals the velocity and if there's no .

Slope so if slope equals zero then the man's not moving at all so here on 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 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 is this .

Mean well first of all it's a slope it's a positive slope and that means the man is moving whereas the man start at position 0 and x 0 and whereas the man end at position 6 and at time 3 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 the man is walking so what's the rise in this well it goes from 0 to 6 and so the rise is going to be 6 meters 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 meters / 3 seconds or 2 meters per second 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 that object so to solve that 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 meters the initial position is 6 meters um the final time is 8 seconds right here and the initial time is 5 seconds and so this should be negative 3 meters divided by well 8 minus 5 is 3 seconds and so during this period of time the speed of the man or velocity is negative 1 meters per second .

And so our speed here was 2 meters per second our heat our speed here is 0 because the man's not moving again and then down here it's negative 1 meter per 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 1 to position 3 so foot position 1 to position 3 what was the velocity the velocity was and let's make this one and make that 2 on our scale so from here to 3 the velocity was actually 2 meters per second 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 2 time 5 is 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 it should be straight vertical ok so the velocity was 2 meters then it was 0 meters per second what was it during this period of time we just calculated it for the next 3 seconds 1 2 3 it was negative 1 meter per second so 1 2 3 it .

Was negative 1 so we'll call this negative 1 right year 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 heap 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 it's just to figure out the slope because if you figure out the slope of the position versus time graph that'll always tell you that the velocity versus time graph if that doesn't make sense go play pH its pH et Colorado edu play with the missing man for 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 that moving man was moving straight to here and then resting and straight to your 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 it's velocity is changing 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 so I hope that's helpful

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