Hey, guys. When you're solving motion problems involving motion graphs, a lot of the times you'll 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 going to do in 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 going to do that here. We've got a motion graph for a moving object. We've got a bunch of lettered points a through g. We have a bunch of questions to solve. It might seem like a lot, but once we get the hang of it, this is actually going to 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 what we're going to 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 are only 3 possibilities. You're talking about the position, the velocity or the speed, which is 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 are only 3 possibilities. So we're going to be looking at the values, the slopes, or the curvatures. To figure out which one of these, we're actually just going to use this table down here that summarizes everything we know about position graphs. On a position graph, remember, the position is going to be on the y-axis. Positive values are here, negative values are here, and you're at 0 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 going to look at here. So we're going to look at the values. So what I like to do is, for each one of these points here, you're basically looking for where you are on the y-axis. So what I like to do is just draw little lines straight down here and the lengths of each these lines is your position. Here at point E, you're on the axis so there is no length. And then f and g look like this. So that's the second step. The third step says now the qualifier. Which qualifier are we going to use? The qualifier is basically just what about the slope are you, or sorry. What about the value are you looking for? We've got this big list here, but every single one of these problems is going to boil down to one of these options. We just 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 axis. So that's when your position is equal to 0. So in this list over here, between positive, negative, 0, up, down, sign changes, maximums, and minimums, the qualifier that we're looking for here is where the value is at 0. So that's the 3rd step. And now the last thing we just have to do is interpret this from the graph. Where are the values equal to 0? And this only happens at 2 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 going to delete that one. And instead, it's just going to be option E. That's the only place where the object is at the origin. That's the 4th step, interpret it from the 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. Well, remember origin means we're going to be looking for the position. Which means, if we're looking for the position, the second step says we're going to 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 is now we're not looking for where it's at the origin, we're looking for where it is farthest away from the origin. And so, in this list here, what does farthest away mean? Well, farthest away means the most. It means the most away from the origin. So now in our list here, it's not going to be positive, negative, or 0, up or down. It's not going to be a sign change. It's going to be the 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 is basically just the lengths of each of these lines. So which line is the longest? Well, it's just this one right up here. It says d. D is the farthest away from the origin. So that's our answer. Cool. Alright. 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 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 going to look at our table down here. So remember that when you are looking for the velocity in a position-time graph, you're actually going to be looking at the slopes of the graph. And there are a couple of rules to remember. Whenever you have positive slopes, like upward slopes like this, you're going to that's going to be a positive velocity. So these are going to be positive velocities. Flat slopes are when you have zero velocity. And then downward slopes are when you have negative velocities. The other thing to remember is that if you have more vertical lines, then you're going faster. The magnitude of this velocity is higher. So if you were to call this V1 and V2, then V IsEthernet higher than V2 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 going to look at the slopes of the graph. So now the third step is the qualifier. So positive or negative, 0, up or down, sign changes, maximums, or minimums. Well, what does again moving forwards mean? Well, moving forwards means you have a positive velocity. And again, from our rules, we know that that's going to happen when your slope is upward. So the qualifier 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 going to draw the slopes really quickly. For A it's going to look like this. At B. At C, and for these curvy parts, you have to draw the tangent lines or the instantaneous. So it's going to look like that. And then F is going to 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 are only 3 points. It's going to be A, C, and G. So those are our three options. So A, C, and G. So that's where we interpret it from the graph. Alright.

So now where's the object moving backward? So again, let's just go through the list of steps really quickly. Moving backward means velocity. Velocity means you're looking at the slope. Now the qualifier. Well, the qualifier for when we were moving forwards was we were looking at upward slopes. Backwards is just going to be the opposite. So now we're just going to look at downward slopes. So now on the graph, where do we have a downward slope? There's actually only one point. It's right here at point E. All the other ones are either upward or flat.