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Conceptual Problems with Position-Time Graphs

Patrick Ford
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Hey, guys, when you're solving motion problems involving motion graphs, a lot of times you have to interpret these graphs to solve some conceptual questions about the position, velocity and acceleration. This can confuse some students because the hardest part is figuring out what exactly you're looking for on the graph. So what I'm gonna do this video is give you a list of steps to follow so that you get the right answer every single time. The best way to do this is actually just by looking at this example together. So we're gonna do that here. We've got a motion graph for a moving object. We've got a bunch of letter points A through G. We've a bunch of questions to solve. Might seem like a lot, but once we get the hang of it, that's actually gonna go pretty quickly. So the first thing the first problem here says at which letter, point or points is the object at the origin. So here's we're gonna do for every single one of these problems. The first thing you have to do is identify which motion variable you're talking about. There's only three possibilities. You're talking about the position the velocity or the speed, which was related and the acceleration. So let's take a look at the problem. Where's the object at the origin? Well, the origin, remember, is just a coordinate. It's a reference point, which you're starting from, so it's a location. So between position, velocity and acceleration, that's actually going to be a position. So that's this first step. The second step says, identify the graph feature. And again, there's only three possibilities. So we're gonna be looking at the values, the slopes or the curvature is to figure out which one of these were actually just gonna use this table down here that summarizes everything we know about position graphs on a position graph. Remember, the position is gonna be in the y axis positive values air here. Negative values air here, and you're zero when you're on the line. And so if you're looking for the position, you're just looking for the values of each of these points. So that's what we're gonna look at here. So we're gonna look at the values. So what I like to do is for each one of these points here you're basically looking for Where are you on the Y axis. So what I like to do is just draw little lines straight down here. And the length of each of these lines is your position here at point you're on the access, so there is no length. And then f n g look like this. So that's the second step. The third step says now, the qualifier, which qualify we're gonna use the qualifier is basically just what about the slope? Are you are sorry? What about the value are you looking for? We've got this big list here, but every single one of these problems is gonna boil down to one of these options. We have to figure out the right one. So we're looking for where the object is at the origin. And remember, the origin is just basically when you're on the access. So that's when your position is equal to zero. So in this list over here between positive negative zero up down sign changes, maximums and minimums, the qualified that we're looking for here is where the value is at zero. So that's the third step. And now the last thing we just have to do is interpret this from the graph. Where are the values equal to zero. And this only happens to two points here where you're at the beginning and then here at point E. But this isn't one of our letter choices. So we're gonna delete that one and instead is just gonna be Option E. That's the only place where the object is at the origin. That's the fourth step. Interpreter from graph. Let's keep going. So now we're supposed to find out where the object is the farthest away from the origin. So let's just go through the list of steps again. First identify which variable we're talking about. Remember, Origin means we're gonna be looking for the position, which means if we're looking for the position, the second step says, we're gonna look at the values. So that's the first two steps right there. And now we have to look at the qualifier. Well, the thing that's different about this problem isn't now we're looking now. We're not looking for where it's at. The origin were looking for where it is farthest away from the origin. And so in this list here, what is farthest away mean? Well, farthest away means the most. It means the most away from the origins. You know, inner list here. It's not gonna be positive. Negative or zero. Up or down, it's gonna be a sign change. It's gonna be a maximum value. So we're actually looking for where the value is the maximum. So now the last step is interpreting it from the graph. So remember that the positions basically just the length of each of these lines. So which lines the longest? Well, it's just this one right up here. It's just D D is the farthest away from the origin. So that's your answer. Cool. All right, let's keep going. So this third part here now is Where is the object moving forwards? So again, let's go through our list of steps. Identify the variable. We have some new keywords here. Now we're talking about moving, and we have forwards, which is a direction. So we're talking about motion and we have a direction. So that means that we're not talking about velocity. We're actually going to be talking about the I'm sorry. We're not talking about the position. We're actually talking about the velocity here, so that's the first step. Now, the second step says Identify the graph feature. And to do that, we're gonna look at our table down here. So remember that when you are looking for the velocity in a position time graph, you're actually gonna be looking at the slopes of the graph. There's a couple of rules to remember. Whenever you have positive slopes like Sorry, upward slopes like this you're going to that's gonna be a positive velocity. So these are gonna be positive velocities, flat slope. So when you have zero velocity and then downward slopes or when you have negative velocities the other thing to remember is that if you have more vertical lines than you're, you're going faster. The magnitude of this velocities higher. So if you were to call this V one and V two than V one is greater than V two because it is a steeper line, so steeper line means faster. So going back to our problem now, where is the object moving forwards? Well, the second step says we're gonna look at the slopes of the graph. So now the third step is the qualifier. So positive or negative? Zero up down sign changes, maximums or minimums. Well, what is again. Moving forwards means well moving forwards means you have positive velocity and again from our rules. We know that that's gonna happen when you slow slope is upward. So the qualify that we're looking for is where the slope is upwards. So that's the third step. Now we just have to go and interpret that from the graph. So we're just gonna draw the slopes really quickly for a it's gonna look like this at be at sea. And for these Kirby parts, you have to draw the tangent lines or the instantaneous. So it's gonna look like that. And then F is gonna look like this because it's at the bottom of the valley and then G looks like that. So where are these slopes? Positive. Well, there's only three points. It's gonna be a C and G. So those are three options. So a, C and G. So that's where you do interpreted from the graph. All right, so now where's the object moving backwards? So again, let's just go through a list of steps really quickly. Moving backwards means velocity. Velocity means you're looking at the slope now. The qualifier. Well, the qualifier for when we're moving forwards was we're looking at upwards. Slopes backwards is gonna be the opposite. So now we're just gonna look at downward slopes. So now in the graph, where do we have a downward slope? There's actually only one point is right here at point E. All the other ones are either upwards or flat. So that's just gonna be pretty straightforward for this last one. Where is the object or sorry for this next one? Where's the object? At rest? Well, at rest. Uh, it means that it's actually not moving at all. So even though it doesn't say moving, we're actually still talking about motion. So we're still talking about the velocity, which means we're still going to look at this slope. And so now the qualifier. Well, remember that when an object is at rest, the velocity is equal to zero. And from our rules for slopes, we know that you have zero velocity when the slope is flat like this. So we're just looking for where the slope is equal to zero or where the slope is flat. So now from the graph, where does that happen? Well, if you look through here, we have a flat slope B, D and F. So that's either the average or the instantaneous velocity doesn't necessarily matter which one. So B, d and F those were answers. So now for these last two, where is the objects? Acceleration. Positive. So now there's in a couple of key words there. So we have acceleration now. So let's go through a list of steps. Which motion variable We're talking about position, velocity, acceleration. It's pretty straightforward. We're gonna be talking about the acceleration. So which graph feature are we going to look for? Well, let's go through our diagram. Our table, if we're looking for the acceleration now in a position time graph were actually looking for, is we're looking at the curvature. So the curvature, whether it's a smiley face or a frowny face, the rules are pretty straightforward. Remember that when you have a smiley face like this, then that's going to be positive acceleration. And when you have a frowny face, that's going to be negative acceleration. So we're looking at acceleration, which means that from our second step, we're looking at the curvature. So now our third step is the qualifier. What qualify? What about the curvature are we looking for? Or remember that positive acceleration, positive acceleration. You means that you're going to have an upward slope. So that's the qualifier we're using here. So where do we have an upward slope? Well, it's actually to be right over here where we have a little smiley face. So the two points over there are F and G. And now, lastly, where's the objects? Acceleration. Negative. Well, now we're looking for acceleration again. Go through the list of steps, which means we're looking at the curvature. And if positive acceleration meant we're looking at upwards slopes or smiley faces, the negative acceleration means we're looking at where the curvature is downwards or frowny face. So that happens at two points here. We're looking at C and D, where you have a little hill like this. This is going to be that a debt downwards curvature. So the two points there are C and D. Those air answers. Alright, guys, hopefully got a lot of practice with this. We have another example that's coming after and let me know if you have any questions