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2. Motion Graphs 1 Position Time Graphs High School And Ap Physics 11: Hey, Moosa. Here, Let's do this. We're talking about motion graphs, Motion graph scraps. In general, I find give students the heebie jeebies for some reason. Uh, and I'm not gonna even go and try to figure out why students want to avoid the interpretation of grabs at all costs. I'm saying this because I need you to not do this graphing in physics. Go hand in hand. You might not have to grab all the time. You might not have to analyze scraps all the time, but it will exist throughout the entire year. In any future years of physics that you may potentially take. Please take the time toe, understand emotion graph. I'm gonna go through a series of videos describing motion graphs than with the kingdom attic problems. But the fundamentals that you're gonna learn from these motion graphs will indeed still exist in future chapters. Stop. Pause it, rewind it. Make sure you firmly grasp motion graphs very, very important and not just motion graphs, but graphs in general. So now we're going to take my graphs of motion, but all likely in the future be grabbing other things. Keep this stuff in mind. Also before I get very far ahead because in physics we tend to utilize real life examples, and we can kind of in some units picture what's happening or even demonstrate what's happening. We, for some reason, want to assume that emotion graph is a visual representation of what we actually see, and it's not necessarily true. You know what I mean? As I go through some examples. But just keep in mind that the interpretation of the graph itself the analyzation of the data and understanding the variances like sloping area. That's what's gonna help you understand the actual and interpret what's actually being graft, not don't just look at the actual graph itself, you know what I mean is they bring this up. So before even talk about the different kinds of motion grabs, I do want to talk about two key terms that you will be having to analyze for most graphs, and that's going to your slope. Masse gave me and it's also the area underneath the slope. Those two things slope and area underneath the slope are very important to analyze when dealing with any graphs and physics, and I would kind of constantly be reminded you about over these next few, uh, lessons. So the first type of motion graph that I want to deal with is gonna be a displacement time graph or a position time graph. However you want to go ahead and think of it on, it's gonna be a displacement variable on me. Why axis? Any time variable on the X axis? I'm gonna go and write that out here. Displacement. I know my penmanship is grand right now in your units for displacement is common. The meter and that's could be on my y axes here and then this is giving time and I'm gonna write this down here. So I'm not fudging with my numbers that I'm get eventually put in. Probably maybe not. I might not put numbers in some of these examples and, of course, times in seconds get displacement versus time. My wife versus X. I needed to understand the displacement sometimes has the variable X given to it or the verbal why'd given to it? Or is he or other variables? And you might think, Oh, X should go on the X axis, but that's not it. This is a coordinate system, X y axes the variable X and nothing to do with the actual axes itself, although it can. Sometimes we'll use X to describe the motion along exact sense, right? Um, and let's talk about dependent versus independent variables. Typically speaking, the horizontal axis is the independent variable. That means this variable does not depend on anything really more or less. It means everything else depends on it. So, dealing with physics graphs and most science graphs, you typically put time on the independent variable. But that's not necessarily always the case. I know some teachers will say Time always goes on the X, and that's probably the case 95% of time. There will be a few examples later on in the year. Where you gonna see that we get to put time on the Why So the thing that doesn't depend on Steph goes here, so time this moves forward, right? One second to second were not gonna change that. Let's stays here. Where the object is does depend on the time, and it's the dependent variable That's the Y axis. Another thing I want to bring to your attention. We don't necessarily refer to this over and over and over and over again. But I will throughout a few of these lessons. So I'm gonna leave it up here for a while on that's our standard linear equation of why equals m X plus B. And just remember a few key things here being the slope. Why being the intercept? Okay. And that's gonna come into play. As I go through some examples, I'm gonna try to connect this equation to the graph, but I won't always. I'm just gonna leave it here for now just to make things simple. So I don't know, Maybe I should just kind of tossed down an example here. So let's say I've got a you know, I'm not even describe. I'm 19. Put numbers here. I'm just gonna show you. So I'm gonna place a wine, you know, I'm gonna go ahead and say that it has this slope. This is the graph. OK, this is my motion graph. The thing, And you're looking at this not having any idea of what motion grabs our and you might be saying yourself. I don't know what I'm seeing here. There's nothing there. There are no numbers. There's no description. How can I make anything out of this. And that's the whole point. I don't want to put numbers in here. I don't even want to explain to you what this scenario is. I want to show you how you can actually get a lot of useful information. Just this right now, okay? And so let's look at here. Like I said, there are two things we often analyze. And for displacement time graph is really only one. And so for displacement time graph often refer to his position time graph. So we're gonna say P versus tea or D vs t A, P T or D T graph these guys position or displacement. So I wrote a boat down the thing that we really need to look at this slope. What is a slope representing now? I don't mean numerically. I mean, like, literally, what variable does this slope represent? And so, for that, we need to dip back into our basic math and we need to say, Well, what is the slope of any graph? Miss Hope of any graph? Whether is the displacement time graph or not will always equal. Think about it. The rise over the run on more appropriately in terms off mathematical graphing skills. You rise Your upper value is your change in your Y variable over your run. You're changing your x variable. So it's actually delta y over dealt X. This is the math version. The physics version we're gonna take Well, whatever physical variable is on the Y axes, replace that on top and what physical variable is on the X axis? We'll look at it. The Y axis is displacement. So I'm gonna say change in not why changing D and the ex I's gonna be time you see a change in time. So for this particular displacement time or for any displacement time graphs the slope will always be your change in D over 10 years and t now think about that. That should bring a bell in your brain. You should be able to remember what that is. Yeah, you perhaps might remember that change in distance over time is actually average velocity. Yes, the slope of a distance, Time graph or position time, Rapper Displacement time graph. Wouldn't ever helps is indeed the velocity. Think about it. That means that I'm gonna write this in here. You don't need to write this And this isn't something that we would normally look for, but I'm gonna put it here just so we don't forget, the slope of this graph represents the velocity. So we should be able to figure out more stuff. Let me erase some of this stuff so I can have some operating room. Well, you think about what you can know in terms of this giving problem. Okay, Velocity time graph. We're not lost him a distance. Time graph, slope being velocity. What do you know about this slope in this example? What do we know about this slope? Well, it's a straight line. And what is this? A slope of straight line represent to you of value? That's not changing. So in this example for this displacement time graph, we know what the velocity is constant. If the velocity is constant, that means the velocity is not changing. Which also tells us this object is not accelerating. Acceleration. Therefore, is zero again. There were no numbers here. I didn't tell you to say at a time you could just look at this and say OK, straight line displacement time graph constant velocity, acceleration zero. Cool. We should also be able to remember a few other tickets in terms of our fundamental understanding of graphs. For example, is this slope positive or negative? Yeah. Hopefully you remember in this case is positive. And if it's positive and it represents velocity, that means the velocity is positive. Which means the object is traveling in the forward direction And whether if that Ford might mean east, it might mean up it might literally mean forward. OK, but you know it. It is here. We do have positive velocity. Cool. I think that's pretty good for now. Um, let me drop down another one on top of this. Now, let me raise this and give a few other examples as we go along and so we can go through a non mathematical approach on identifying this stuff right here. Let me you race this board one second. Actually, you know what? Just as I was reaching for my clock over. Donna, do want to point out this thing here. Do you see how I started this graph? This plot? Not at the origin. It's not a zero. This white intercept means something to remember in this example. The why is the displacement Uh Let's go back to this equation here. Why? Bam? Right here. This means that whatever this object Waas began, we began collecting data at a non zero starting. So we would actually say in this example the initial X value. The initial X value is not actually zero. And so if the object started, if I were to do a position timeline 0123 or all way down, just housing random numbers in here. The object started here, and I would plot it. Zero. But in this case, the epic story in a non zero spot. That's why it was up here. Okay, let me raise this board and let's go through a couple others. I increased my time. I want to keep that there, don't I? My actual graphics turn the race away too. Okay, So time back down there and bottom. Let's look at a different example. Go here, Start here and do like this. What does this mean? Interesting. First of all, I'm proud of myself making that nice curve like that. I don't usually do that. It gets all on Whatever. Okay, so remember motion graft, displacement time, slope means what? Yes, Slope means velocity. What can you tell me about the slope in this example? Is the slope still constant? No, it's not, is it? It's not a straight line. And here the slope is changing now, So they want to bring to your attention here. And is this concept of instantaneous velocity. So the slope of this graph represents of loss. And we see that this lawsuit is changing, Which means we know that in any given moment time the blast, you will be different than any other moment in time, or at least on average, so well, so we can't quantify right now without using some decent math skills. So just conceptually, we can't quantify the velocity. Anyone? We could still get an idea of whether or not this object is increasing or decreasing speed throughout time. And there's this term that we want to look at called a tangent line. And you may recall from math and I'm gonna draw one, and then I'm gonna erase it or not. You re so I'll just leave it there. And then I use my ruler. You may recall, in math, a tangent line is any line that touches a curve. But only touches at one point, so I won't bisect that line not only touch at one single point. So if I took my ruler and I place that like here, this rulers touching two points, that is not a tangent line. But if I take this ruler and I touched just one single point, that is attention line. So if I were to try to draw a tangent spot at that spot right here, what's that black line right there at that instant? The slope is a moderate value. But if you were to look later on spot tangent to that curve right here, that slope is indeed steeper. And if you're look early on that slope is pretty shell up and so far to take that ruler and move it along that curve tangent to the curve. You will see that I'm hitting the border of my board, but also you will see that that ruler is getting steeper and steeper and steeper, so that should indicate to you the velocities increases. Which means if the velocity is increasing in the forward sense, that means acceleration. Acting on this must be non zero right Changing slope slope represents classy changing Boston must be an acceleration. And that acceleration is indeed positive because the velocity is also getting more positive . So here we have a positive A which is causing your velocity to increase Cool, Right? And again, you can tell by just looking at the tangent line. Early on, we had no slope, but also what was my initial starting velocity of this object? Big Zero. We had a nice constant acceleration acting on it. Damn. Now, non constant accelerations are very rare in physics. Let me just quickly try to show you what it may look like. That would be a scenario in which my line is disappearing. Oh, well, it would be a scenario in which the, uh, curve will be a non consistent curb. So maybe it starts off as a nice curve. A minute starts to change curves again. We're not gonna quantify this, at least not in these early physics classes. But you will indeed able to tell that the A has to be changing because we don't have a nice , consistent curb way up. So here, acceleration served to shift. And in fact, we can look at it. We considers positive acceleration here, and then here the objects start off with a nice high speed, right? And then I get mad, Tanja. And that velocity started the decrease. Decrease, decrease, decrease, decrease, decrease. And then, bam! We're actually at zero. You see, on my slope, the top is Where is I mean zero velocity here. So that's interesting, right? Right there. V is zero. And right here at the peak of this curve, the velocity is also zero. Here. The V is very large. Here you have zero. Here we have zero. Okay And all has to do with the fact that there's a changing celebration because now, after that zero spot, that velocity is starting to decrease. Quite quite a bit, actually. Right. It's negative velocity now, while decreases and goes more negative. So it's actually increasing magnitude in the negative direction, right? And then it's so now it's starting to slow down. Getting back to zero velocity the slope throughout this graph you're not gonna quantify, but you should be able to point out those areas. Give a few more on their way to wrap this one up. We're talking about the next video, your type of velocity time graphs, which will look very similar, but mean, completely different things. Hence you can't just look at that. You actually have to interpret Were like, What is this guy? Let's see Stirred up here. Let's take a look at this guy. So this here is an object that starts in some initial positive displacement. So we're starting in the positive spot away from zero. It is going to approach zero throughout time, so it's gonna be heading back towards the zero spot, and then once it gets here, it's gonna keep going backwards further away from the zero spot. So if I were to maybe put a displacement kind of position line down here, I use a word for that on. I'll call this the zero spot. Maybe up here. This person started here, right? And then we see at this moment in time, we're at at zero position. So this person started going start to go backwards, right? And then when they get back to the zero spot there now, in the negative portion of this graph, I may be finishing somewhere over here. I'm not trying not to put numbers in. They finished in the negative region. The graft, I hope you remember that this is a positive region. The graph. This is the negative regional crap. It's back, Back in your math classes. I hope you're recalling some of these math skills that you are supposed to have retained forever. Right? Uh and so what does that mean? If a dude starts a deposit spot or do that, I don't want to offend anybody. If the dude slash do debts that it's in a positive position, it starts to go back to the negative position. Shouldn't imply that they are experiencing negative velocity yet. They are so essentially reset a while ago, it hopefully didn't break that down. That was all carry over from the last example. Right. So in this example, the A zero. Why? Don't know the acceleration zero. Is the object accelerating? No, because we have a non changing slope. So we have V is constant, and we also know that V must be negative. Cool. I hope your understanding this I hope you're getting this. It's very, very important to really build interpret motion graphs. I'm gonna go through an example worksheet where I kind of give a few other clear examples on this using actual numbers and, you know, real life scenarios. Um, and there's all sorts of others. I'm not getting a whole lot of time. You've got this kind of curve. Starts off with zero, but now is approaching a negative high velocity. So down here, we have negative high velocity. Here we have zero velocity, and then somewhere in here is a negative moderate velocity. Which means we do have a constant soldiers and acting on it. Um, no, you'll probably see many, many more. So stop. Don't just memorize these. Just think about how to interpret it. Okay? I think that's gonna be a good a good time to wrap up this video next video. We're talking about the velocity time graphs.
3. Motion Graphs 2 Velocity Time Graphs High School And Ap Physics 12: Yo, move. So here, let's continue this motion graph. Talk. Uh, this. But I'm gonna cover velocity time graphs depending how long it takes someone just getting exploration time grabs as well, because they're really not to difficulties. But the emphasis on this video, the majority of it will be velocity time graphs. So let's do this. Were put velocity on the Y axis. Okay. Be like very well during one of my units for velocity? Yep, meter per second. And then time down here. Still seconds. Still the independent variable and being on me X axes. So I'm gonna go ahead and just do something to the last one. Toss a few lines on here and try to make sure I'm interpreted. So we'll start off with a nice basic one on, and we're gonna have this guy right here. And what is this that represent? Now just is the case with all grabs. First things first. Identify what the heck is sloping. Remember, slope is rise over run, which is changing. Why? Over change in X, which in physics is the change in the UAE. Variable over the change of the expert, which is give me change in velocity over change in time. Mm. What has changed? Velocity over change in time, but equal. You can remember that one. Yep. Acceleration a velocity. Time graphs. The slope is indeed representing acceleration. Cool. But before even start talking about what is the slope of this craft? There's another thing that we need to look at for velocity time graphs. And this is the case for a lot of graphs. So it's always sloping. In the last year, I told another one you want to look at is area We didn't discuss the area of a displacement time graph. Too much was it doesn't really mean much in terms of physics, but velocity time graph. It does. So the area under this slope means something. And so, you know, every time you take in the area, you always take it the area underneath the slope itself. Okay? Something about this whole region here and again. I'm not putting numbers in, so it might be difficult to quantify this, but that whole region here is the area I'm talking about. So I don't worry about this area up here or anything below the axes here. It's always give me from the slope to the axis. So now that slope drops into the negative region or be from that slope above. It's between the slump in the axes overs, and I'll give an example for that shortly. So what is the area of this graph represent? Well, how do I find the area of anything? Well, let's look at my basic geometry here in this example. Here I look at the shape in this shape. Looks like a triangle. And so, in this example, the area is 1/2 of my base times my height. Well, what is my base? Actually, I'm not great. Be times age. That's maquettes geometry. They use weird letters to use real physical step. What is this time looking at 1/2 of time times, height, velocity, 1/2 of TV. What's weird, right? This might not be very clear to you what I am showing you. So I'm gonna kind of show you what I'm trying to show you and then connect the two together . And really, what I needed understand, is the area underneath the velocity time graph is indeed displacement. What? Yes. Think about it. Average velocity is changed in distance over time. If I were to isolate displacement. The displacement is average velocity times, time tee times here every time, Steve. But you know, switching around Matt for you. So this actually represents the total displacement. So where is that 1/2 come from? With only reason when half is there because it's a triangle. I'll give an example where it's not a trying when you can understand why that one happens Needed. But for now, just recognize the area of a velocity Time graph is indeed displacement and a few things that add to you. If my area isn't deposit regional graft and I posit displacement s means this object is moving further away from zero position. Cool. If my areas in the negative region the Grafton, I have negative displacing. Which means that that during that period of time they were headed in the negative direction . If you have a overall positive net area than you've moved further away from the starting position, given overall negative net area, then you move so left or in the backwards of the starting position. And I will break that down An example video shortly. Probably. The next video will be a series of examples where Actually used numbers for now. I just want that concept in there. Okay, So area is displacement. Slope is acceleration. So in this example, what do I know? I know that I have a constant slope, which means I have a constant acceleration. I also know that that acceleration is positive because my slope is positive. If I have a constant acceleration, that means my velocity is indeed increasing. Well, as long as they start off on deposit or finished in. Positive symptoms did. But it was over here in this portion. The graph I could have been decreasing momentarily. So glossy is increasing. Cool. That's really basics. Let's go through a few other examples just to make sure we can see through the difficulties . And what I'm just gonna do is kind of expand on this already existing graph. I'm gonna leave what I have. They're just add a little bit more to it. I'm gonna show a scenario in which well narrated yet and this if you're doing this at home , you might want to just do This is a whole new example. Don't add to the urgings already existing example because it might be kind of All right. What do we got here? Let's break it down here beginning. Same thing here. We still have that positive except positive. Constant acceleration. What's true about my slope during this Pete period right here? No. A zero. No slope. What's true about the slope here? Constant and negative. So a is negative practices my help separate my assembles. Not only that, I can also kind of compare the magnitude of this slope to this slope. Most This is negative. It's also steeper. So I have a larger magnitude of acceleration. And it's in the negative direction that I did earlier on where it was relatively moderate. Magnitude of acceleration. Positive. Remember, the area underneath the slope is also important. So I wanted to show you this geometry here. Perhaps you can see that middle region. I'm gonna pick a different color here, so pops out a little bit more. Perhaps you could see his middle region. His best shown is erecting or square on. I don't know. I think that this is a pretty clear triangle right here. I remember. I go up to the axes. This is all positive displacement, men. We've got this last bit on a swell changed color. I don't want any of you all to get upset with me. Don't do that. So I'm gonna go ahead and say, Miss here this last segment and I stopped with line stop, so I'm not gonna just fill us in infinitely. That's kind of silly explaining what we've got going on here. Here we go. We got an object that starts off with zero velocity. It's good experience, a positive acceleration, and see to get further away from a starting position. So it's gonna increase positive displacement. It's very good to travel during this segment with constant blah six. There's no acceleration, no acceleration. Doesn't mean no speed. In fact, here we've got a pretty high speed. Whatever this number represents a pretty high speed. So it's still moving forward. But now it's moving forward constantly. So this whole area is still positive displacement. So perhaps it started off slow. I don't know. It was all like, slow. That is increasing, increase increasing speed. And then it's nice, constant speed, that last maximum speed. And then at this spot, what starts to happen to it starts experienced negative acceleration. Remember, this spot was already moving in the positive direction has a high positive velocity. It's experiencing a negative velocity, so whilst it will continue to move forward, it's gonna begin to slow down. So during this next segment, it's increasing in displacement, so it's still positive area. Positive space matter. A positive review in the graph, but it's slowing down until we get back to what is this value of velocity back to the origin. So right here we have zero boss in my eyes Will put that in there. Right here we have V is zero. Here we have just be is zero. So this whole time, we had some positive all city, and that was slowing down slowing. And now it's back to the beginning of its original velocity. But so far away, You know what travel during that whole time. Then it starts to continue to experience that negative acceleration. So now that it stopped, it's gonna actually start to head back toward where it came from during this region, Pence, this here is negative displacement. It's actually going backwards. Okay, so this whole time I was going forward, and this time it's going backward. Now, if we were to do some math here If I were to take all of the positive region and then add it or subtract the negative region from its if my final value remains positive in the object finished at a location positive from where it began. If the overall net value is negative, that means the object finished behind where it began. You can probably tell I'm not quantifying it, but you can probably tell that there is more area here and there is right here. So it's still is gonna finish someplace further away from where it started. Pretty clear, right? I don't know. I think it's pretty clear. I hope it's pretty clear going to give you one more quick example. And then we're gonna get into acceleration time drafts. I'm also looking at the time here and I don't know. I'm already at, like, 10 someone minutes. I think I'm gonna break after this one and then just do acceleration time graph is its own separate. Think that makes the most sense? So what's you have one last quick example? We haven't seen the curve yet, so that's just what I want to drop down. Here is what it looks like and you know as the case, which will be the in all of physics throughout the whole year. Really, In all of these video lessons, there is no way I could give you every single example you can't just say here and memorize every possible example. And then just, you know, again just memorized the answers. You have to actually think this stuff through. So you know, I'm not going through every possible example for a reason. But let's say we have some of this curve. All right, Cool. So what's happening? What does this mean? Well, let's think about it again. Where there's a slope of a velocity time graph represents what has changed to be over changing t up its acceleration. So my slope is changing, so I have a changing acceleration. So here we're talking non constant. This is rare in entry level physics classes, high school physics classes so mathematically we won't have to analyze this, but graphically, we should be able to interpret this. We do know that it's accelerations, non constant. In fact, it's acceleration is going from a low value of acceleration to it. Just remember to do that Tanja line. Think Tangela and being tange Olympic. We have a very high final exploration. So at this point time, it's it's it's got a great acceleration. That means it's getting increase in velocity uh, mawr per given second here than it did down here. That can should make sense of things about 1234 Maybe five seconds later, its velocity only went on one notch, provided to five more seconds. 12345 Here its velocity went two or three notches in this spot right here. This velocity is going, Ah, significant increases. We're gonna get more, more, more really picking up. Ah, whole lot of speed. Here and again, we can take a look at that area of the graph. This is where mathematically, it's to be quite improbable to do without some understanding of calculus. So we're not gonna do that to you, but recognize that if I were to take just a given segment here this given a few seconds here, compared the next few seconds we're covering Maurin Mawr displacement throughout this time so far to break this down, let's say two second intervals, so that looks like two seconds. That's two seconds. That's two seconds two seconds to say second those columns. Sorry. I like to make noises. You can see here during this. I don't know. Just for comparison's sake, I'll just say Segment A, B, C, D E f and G. I know my alphabet. Yep. I have a couple of young boys and home, and we've been practicing me off a bit over the last. A couple of years. Actually. My oldest is turning three soon. In any event, here we go. We've got in segment a very little displacement because it wasn't going very fast. By the end of Satan, a man segment d we start to get a decent amount of space and enduring segment G. Those last two seconds it covered a great amount of distance in the same period of time is the prior two seconds That's good. Is going faster and faster. Faster, Faster Because it's got increasing acceleration. Oh, okay. Velocity time graphs help. You got it. Remember, recap Slope is acceleration. Area is displacement. Cool. Thank you.
4. Motion Graphs 3 Acceleration, Velocity, And Position High School And Ap Physics 13: All right, Moussa, Here, continue our topic of commotion graphs. This video is gonna be all about celebration time, grass. But, Dennis, with you, their basic boring some just get explaining celebration time graphs while also comparing some scenarios of displacement. Time graph in Boston Tenders. Whatever guy. Here's three different grabs. Kind of on top of each other vertically. You see this a lot in physics problems? Ah, we're up here are gonna be modeling the displacement of the object here. I'm gonna be modeling the velocity and the down here, the acceleration acting on. I'm gonna give a couple of different examples so you can try to make sense of all of this. And remember, the key things look at on each graph of the slope in the area of each, whenever we possibly can. Okay, um, we're so let's start off with the basic of basic. I mean, what the most basic one? Let's get a little bit. Um, let's mix it up a little bit and I'm gonna give you this situation. And I'm not gonna again I'm not gonna put specific quantity in here and just kind of say, like, medium versus large, and we're gonna go with it. So what I want to show here and then I want to see what the V graph looks like. 80 graph Looks like. So here we've got herself of the displacement time graph. You can see here that it objects started at some positive displacement approach. The zero spot finished that. Some negative displacements, you may recall, that means the object is going backward. Let's take a look at the slope. The slope represents velocity, right? It's a displacement time graph. I have the time. We down here instead of me. Ready crimes. And here, displacement time graph represents Lopez Lopez. Constant is negative, so I have a constant velocity. That's negative. It doesn't look all that high you have. The slope is pretty shell. Remember, horizontal zero vertical is infinitely high, so we've got ourselves a pretty shallow speed and it's a negative speed and it's constant. So if I were to go, then go ahead and model the velocity time graph. I need to have a graph that shows constant velocity will remember for a velocity Time graphs. The slope represents the acceleration, and if we're in dealing with constant velocity, that means there is no acceleration. So I should have once again, not on Lee A constant slope. But now, in this case, that constant slope should be zero. That doesn't mean I'm zero on the X axes. That means I should have a slope of zero value. Remember horizontal zero slope. So it's almost have a horizontal line. I'm representing constant velocity. When I'm dealing with a velocity time graph, we know that that glass is negative. And like I said, moderate. So what I'm gonna do just, you know, randomly without tossing numbers in here, I'm gonna draw a horizontal line in the negative region of the velocity time graph. That means this object is experiencing during that entire segment. So if I were dashed down here, I can see that this represents the same moment in time for all three graphs, right? Or to dash down at that spot. That's where it ends. Constant negative velocity, constant negative losses. Cool. Now it's like about the acceleration time graph, and this is why I said it's election time. Graphs are kind of boring because entry level physics, high school or AP style physics, we typically deal with scenarios in which we have a non are a constant acceleration. Member uniforms are in motion, so we have an acceleration that's always give me the same. So almost every single time we do an acceleration time graph. Unless it's a conceptual type of scenario, we're gonna be dealing with horrors on Alliance. If we have a horizontal line at the origin, that means acceleration 05 a horizontal line above the origin. That means acceleration is positive. And if I have a below its negative, So we see here from looking at the velocity time graph or even looking at the displacement time graph that we have no exhilaration, all its constant. So I need to draw a line that represents zero acceleration the entire time. Yet you probably see it pretty boring. I'm just to be drawing a line on the origin, which is getting me. And I'm gonna have to redraw my ex axes once I erase all of this because it's gonna have to happen once the reason is gone. Right, So there we go. Look at how incredible this is, right? I mean, I know you look at it and you might think, Oh, this is boring or I don't know why I have to do this. Once you start doing labs and stuff, this is give you a little bit more clear. I think modelling the motion visa via graph is incredibly important. We do it all the time. In the real world. It's not just in class again. Look at it. Constant negative velocity, constant negative velocity. No celebration. Okay, let's go ahead and give a slightly more. I don't know if it's complex, per se, but we'll kick it up a notch. Okay, Give me a second to erase all of this stuff and used marker end. So I use a Sharpie marker on the marker board so I don't constantly erase it. Right. Which is cool was I like sweet? I don't have to redo my lines over again. But then I have forgot the non Sharpie markers. These dry erase markers. They have little alcohol in them and it makes it so It you races, the Sharpie markers will tip for you. If you ever drawing a marker board with Sharpie marker, you don't have any dry erase board marker Expo marker stuff for the alcohol based cleaning board stuff like this. Product placement No, I'm getting I'm not getting a sponsorship from then. That'd be cool. Calm Expo. In any event, if you just go back over the top of it again with a dry erase marker and then you wipe it erases it anyhow. Wow. Cool. Do you want more than just physics in these lessons? All right. A displacement time graph. Ah, this time I'm gonna go ahead and make a curb so we can see how that translates into the other two graphs, and so I'm gonna show you. Curve. I'm gonna try to curb it all way out to this dash line here, and we'll see if I could make that one of a curve. Not too bad. It was pretty gay. Sweet. We think I practice this at a time, and I did not. Okay, so now here we go. We've got a displacement time graph. We've got nice looking curve. No longer is at constant velocity. Let's get rid of that. Because, remember, the slope of a displacement time graph is indeed accelerator. Hex origin is indeed velocity. So the slope is constantly changing, which means the velocity is changing, Which means the velocity uh, it well I'll say, is increasing this case because we're getting further away from the zero position, which means A is present. It's positive in this example. And I'm gonna tell you it is indeed constant. You can tell us, Khan success. Nice, smooth curve. It's not going up and down and all sorts of directions. So how would we grab the velocity time graph for that? Cause? Think about the velocity is increasing. We're starting out with a shallow slope and then a higher and higher and higher and higher and higher slope. Right, Which means I need to have a velocity. It starts low, in fact, zero and finishes high, but it needs to have a constant acceleration. So I'm looking at my losses time graph. That's just nuts. This is helping. Sorry. Uh, by looking at my velocity time graph, something would cost an acceleration means I need to have a constant slope. Remember the slope of WASI time graph is acceleration, so I need to draw a line of constant slope that begins at 00 The tangent here is zero to horizontal and begins at a pretty high value. It's a pretty moderately high value soul ready It's gonna be amazing. I am going to draw a straight wine. That's not horizontal. Bam! There it is. How about that? And if I were to have isolated, as I could see from there, I have constant acceleration, said Constance Le and its positives positive? A of constant value like that. I'm blending my colors, making call new colors. Lastly, let's do my acceleration time graph. And again, I have constant acceleration. It's positive. So all I need to do down here is have a horizontal line because it's constant with positive somewhere tossed. That sucker rates this number. Do something like this. Bam. Non numerical scores. If I had numbers in here and build a place it more appropriately, but I think this is pretty appropriate. Okay. I think that's gonna wrap up everything for motion graphs. I'm gonna go through a series of examples with a little bit more quantity to him in the next video. I hope this helped. I'm gonna wrap this up now. Thank you.
5. Motion Graphs 4 Example Problems High School And Ap Physics 14: eight Moussa here, let's do a motion graph. Example Problem. You got the problem over here if you can't see it. Very well. Read it out loud. Any I've got the graph set up. It's a velocity time graph. So we've got this velocity time graph for a world class track sprinter in a 100 meter race . We want to know the average velocity for the 1st 4 seconds. We Then we want to know the instantaneous velocity at the T equals five seconds with that one instant. What is the average acceleration between zero and four seconds. What is the displacement from 2 to 4 seconds than finally, What is the total displacement? My work's gonna be all over the place. I might not have enough room for everything, so I might after your way. Some, uh, try to write this stuff down as you go is well, that way, if I do your race, you can still refer back to it. So here we go. Why? We want to know the average velocity during the 1st 4 seconds. So during this fourth seconds, what is the average velocity? This is not anything to do with the graph. as much as the other problems per se. I mean, you need to look at the graph to figure out some values, but this is just gonna be straight up. Average velocity is the sum of each velocity divided by the total velocities. We could do this because we know that they're experiencing a constant uniform accelerated motion and so we can use one of our kinetic equations. We know the velocity beginning has got to be zero. We know the velocity of the internet. Four seconds is 12 meters per second. We just got to come over here and look at the 12. So we're not calculating Sloper area or anything like that. So my average velocity is gonna be zero plus 12 meters per second, divided by two. Gonna find out that I have an average velocity of six meters per second during the 1st 4 seconds. Cool. Be What is the instantaneous velocity at the 5th 2nd? So, for that we just got a look at a graph because this is a velocity time graph. All we gotta do is find where the line is at five seconds and just come on over here to the graph to see that at at the 5th 2nd have lost 12 meters per second. So these 1st 2 because V five causes the 5th 2nd? No, after you just makes sense. The 1st 2 aren't utilizing anything new or groundbreaking in terms of analyzing graphs. It's just simply looking at the time. What are the data line sees? Where it starts to change a little bit? I wouldn't call it making a difficult per se just different, and we want to know the acceleration between zero and four seconds. For that, we've got to recognize how to find acceleration on a velocity time graph. Remember, the first thing you do is identify with what does slope represent. The second thing you do is identify what does the area represent. So in this case, we're talking about the slope of this line from 0 to 4 seconds on the slope of anything is get me to change in the UAE variable. So the change in V, the change in the X ray, which is a change in time. So for C, it's a fancy way of saying what is the slope of the graph? Because change of velocity over changing time is acceleration. So see, just says slope, that'll be changing. Be over changing T. You know the changing be from 0 to 4 seconds. It's gonna be what We're going from 0 to 12 meters per 2nd 12 minutes. Here it was 12 meters per second. You should write that in those 12 meters per second, minus zero all over that change in time, which will be four seconds minus zero now beginning zero. It's really can't 12 the bottom before where you get three meters per second squared for my acceleration between zero and four seconds. Cool. De. What is the displacement from 2 to 4 seconds. This is a little tricky because it's not including this beginning portion or the end portion we're looking at. How far do they travel? Just between two and four seconds. Remember, the area under a slope for a velocity time graph is displacement. So for that, we're gonna figure out the area between the second and 4th 2nd This segment right here. We gotta find this area, and I see two very clear shapes here. I see this triangle up here in this rectangle down here, so I'm gonna find the area of each of these and then just add them together. I'll do my work for D right up top here. I'm gonna first fine this triangle mental. Find this rectangle. I don't care what you do, which when you do first. So the triangle would be 1/2 base times height, while the base is too too forced too. And the height looks like I'm going from six 2 12 So this could be 1/2 of to, And then the height 6 to 12 is six rate. So 1/2 of two times six, it's gonna be six meters. I've got ad that should be displacement for this rectangle, which is simply to be two times six. So that's what 12 meters looks like. I'm getting a displacement of 18 meters with the same pretty straightforward stuff. All right, men E, what is the total displacement? Do that work down here. Total displacement. We need to add this displacement here, but we also need to account for this this additional displacement and then this whole region here it's all in the positive region. The graph, so we simply just add it all up, so e it's gonna be 18 meters. Just this segment were calculated. Waas this triangle 1/2 of based time site, the basis to the highest six. So that's gonna be six meters, right? Plus this entire rectangle over here. So it's going from 4 to 10. It's Let's six times 12. What's six times 12. 72 And it all up with 96 96 meters is the displacement for that segment, right? This is pretty straightforward stuff, you know, in the regular high school creaking. You probably won't be asked to do all of this. Probably have to do this parts of this, but certainly nothing wrong with learning how to do it all because we're gonna have to eventually do all of it in some capacity. And that'll be it for this problem. Let's move onto the next one. We're gonna erase the board. All right, here we go. I got the other problem set up. Um, walking through away guy here. Here's the problem. Over here. Graph below. Over here shows the displacement graph for a particle for five seconds. Actually, Looks like it's going six seconds, huh? Well, OK, so it's always 1/6 6th 2nd and we all we gotta do is draw the corresponding velocity time graph and acceleration time grab. So I kind of put these in here. We just got to go down the line as we do it. Uh, we're gonna attack the velocity time graph. First, let's give you the bulk of our work in the graphic, and then we'll address the acceleration time graph after. So to do this problem, remember For a position time graph the slope represents velocity. So what I encourage you to do is recognize that there's 1234 different spots of constant slope fine the slope for each of those spots. And that'll be the velocity during those segments. So, for example, under to find the velocity from time equals zero time to, and that will be the slope of my position. Time graph. And so it would be my change in distance over my change in time from a change in displacement is going to be three meters over two seconds. I'm gonna find out during that segment. Can I squeeze that in there? Yeah, I can. Two divided by three is 1.5, right, re divided by two 1.5 meters per second probably should have dropped in a line, but that it's a great positive positive slope and finalize initial three minus zero. Makes positive. Now I'm gonna do segment. Looks like this is just from this whole steep slope is from segment to from time to time three. Some would say t two t three. My slope is going to be the change in displacement during that period of time. But by the time of course, final minus initials were finishing at negative 300. Right this one out. So negative three meters minus my initial value, which is positive three meters all over. The change in time. One second. So negative three minus three is negative. Six. We're doing with net negative six. Divided by one of course meters for a second. That makes sense. We can analyze a few things here. We see that it's definitely negative slope, and that's a little bit significantly more steep in the first segment, so it should be in greater value. Awesome. Now let's get segment 3 to 5. You'll notice your position isn't changing, which means the object isn't going anywhere, which means the velocity zero, and you could tell of lost easy artist, but looking at the slope zero slope there it's a horizontal life. So from T equals three t equals five slope equals zero. So the velocity zero now are we. And last bit is that segment t six her t five to t six and we're looking at a scenario where we're going from again. Final minus initial. I only read it out. Slope change in displacement over time. My final displacements in negative too. So negative two meters minus my initial displacement of negative three, some minus negative. Three means plus three. That is indeed just one second her yet that's just one second. So negative two plus three gets us to positive 11 by one. We're looking at one meter per second velocity. Now that I know the values, I'm gonna draw the value corresponding to in the bossy time graph and something recognized . This is everywhere we have a straight line is constant velocity. So every one of these is dealing with constant velocity. So we're just looking at Well, you'll see you probably already know. So during the first T seconds, we were traveling 1.5 meters per second. So during the 1st 2 seconds, we were traveling 1.5 meters per second. So it's just a nice words online because it's gotta have constant velocity of us. Can't change During the next second, we were at negative six meters per second. And of course, yeah. Look what I did here. I didn't give myself enough room. Right? That's frustrating. Well, I guess I can change these. The tea for six. That would put this blue line down here. Yeah, so I'm gonna have to do Sorry about that. If you already wrote this at home or change these so it is 246 This is negative to negative four and negative six. Yeah, that's frustrating. So really, this first thing that 1.5 is what about here? Estimating here for two seconds, issued a mess. Then the negative six from 2 to 3 is way down here. So this will gap with break and then 5 to 6 seconds or no, I'm sorry. From 3 to 5 seconds, we have zero slow. Samir. Do this and then from 5 to 6 seconds, we have one meter per seconds. That's you can Probably if I would have done this again. I span this axes at a little bit more so you can see that these are not all in the same space. And I think it's the showing up. Okay, The acceleration time graph is a little longer because we're dealing with, like, a very brief, instantaneous acceleration at the point where the slopes are changing very brief, instantaneous acceleration. So from here to here, we look up something must have heard it to move it. Uh, from here to here, something briefly impacted it again here, in here so we could calculate that acceleration as it approaches Europe. But that's a math that we don't really have to do in the internal intro level, high school physics courses. So it's relatively appropriate to say that zero acceleration everywhere, like this segment, no slopes of definitely zero acceleration. You know, we're gonna have zero acceleration, although to six. But you might have a little point gap at these spots as you approach zero. But if we were to be taking our basic math that we should know, there's technically no time here, so anything divided by zero is gonna be improbable. Very difficult to solve for right? So we're gonna ignore those breaks. This is my acceleration time. There was no true acceleration acting for a long period of time. All right. I hope these two example problems helped. Obviously, you are encouraged to practice. Practice, practice as many as possible. So use your resource is cool. That's it. Thank you.