2. 1D Motion / Kinematics
Conceptual Problems with Velocity-Time Graphs
Conceptual Problems with Velocity-Time Graphs
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Hey, guys. So oftentimes you need to use velocity time graphs now to interpret them and then solve some conceptual questions about the position, velocity and acceleration. This is gonna be very, very similar to how we dealt with this with position time graphs. We're gonna use the same exact list of steps here. So let's just go ahead and work out this example together. Let's get to it. So we have a box, and instead of a position time graph Now we have a velocity time graph, and we have a bunch of questions. Let's just start with the first one. Where is the box gonna be moving forwards. So let's go to our steps were always going to figure out which variable we're working with. First Isa position, velocity or acceleration. Well, now here we have motion and we have a direction moving forwards. So that means that we're gonna look at the velocity here, So that's the first step. The second step is now, toe, identify which graph feature we're gonna use. And to do that we go down to our table now. When we looked at velocity for the position time graph, we looked at the slope. You have to be very careful here because we're working with a velocity time graph. So here, if you want velocity, value, the velocities You actually just look at the values. This is kind of like how, when we looked at a position time graph, the position was just the values. Well, for a velocity time graph, the velocity is just the values. Okay, so that's why we're gonna look at here. We're gonna look at the values, and the rules are just gonna be the exact same here as they are here. Anytime you're above the X axis, those air positive values and below their negative values. And then when you're on the axis, that's gonna be zero. So it's the same exact rules that you can borrow from there. Okay, so that's the step. We're gonna be looking at the values, not the slopes. Be careful with that. So, which qualifier are we going to use? That's gonna be step three. Um, Well, so first step three, which qualifiers we're gonna use well moving forwards. What is it for words Mean in terms of velocity forwards means that you are who have a positive velocity backwards means you have a negative velocity. So in this list of qualifiers that we have here, we're just gonna be looking for this one where the velocity values are positive. So now that's the third step. We just have to interpret it from the graph. And again, remember that the values are just where you are on the Y axis. And when you're above the X axis like this, those air positive values when you're below the time axis, that's gonna be negative values. So where is where do we have positive values at B, C and D Anytime you're above that access there, so B C and D. Okay, so now where's the box moving backwards? Well, guys, it's the same exact list of steps we know we're talking about velocity because we're talking about moving backwards. We know that we're gonna look at the values because we're talking about a velocity time graph. So now what about the qualifier forwards meant we looked at positive values. So backwards means we're gonna look at negative values. So where does that happen on the graph? Well, that happens any time. Your below the time access. So that's a F and G those are answers. Okay, so that's pretty straightforward. So now where is the box gonna be? At rest. Well, what is at rest mean? Remember, at rest means that your velocity is equal to zero. So which variable we're talking about? We're talking about the velocity. What does that mean? In terms of the element we're looking at the values. And now for the qualifier, which qualifier makes the most sense? Well, guys, we just said that at rest means zero. So the qualified we look for is just where the value of the velocity is equal to zero. So look through the graph and you'll notice that there's two points here where the velocity is equal to zero, which means that we're on the access that happens at two places right here and then also right here. Now, this isn't one of our letter choices, So that means that he is our option. So that's E. And that's our answer Choice. Now moving on, where is the box gonna be turning around? We've seen that expression before. What is turning around actually mean? Turning around means you're moving in one direction. You stop and you turn around and move in the opposite direction. So we're talking about motion in directions. That's gonna be the velocity. So that means we're gonna be looking at the values that steps two and three. Now we just have to look at the qualifier. Which qualifier makes the most sense? Well, again, what is turning around mean means you're moving in one direction. You stop and you turn around the opposite direction. So it's a direction change. And remember, in for velocity, the direction is controlled by the sign. So if you're changing directions, that actually means that you're changing signs. So that's what we're gonna look at here. We're gonna look at where the values change signs. So on the graph now, we just have to interpret where that is again. Remember, these are positive values when you're above the axis and negative values were below the time axis. So when you're change, values is just basically where you cross the axis. Whether you go from down to up or up to down, you're crossing the axis and therefore you're changing signs and changing directions. So this happens actually at point E. It also happens here again, but that's not really one of our answer choices. So the letter e is momentarily where is at rest, and also it's where it's turning around. All right, so hopefully that makes sense. Now let's move on to the fifth one. Where is the boxes? Acceleration. Positive. So go through your list of steps again. We're talking about positive acceleration. Which variable are we talking about? That's gonna be the acceleration. So now what does that mean in terms of the graph elements? What are we gonna be looking for here? So we've got acceleration. So now which one are we looking for? Value Slope or curvature? Well, let's go down to our our table. Let's go down to our table over here for the position. Time graphs. When we looked at acceleration, we looked at the curvature of the graphs. We have to be very careful here because now we're talking about velocity time graphs. So that means that we actually are looking for the slope of the graph in the same way that the slope of the loss of the slope of the position graph was the velocity. So it's the same sort of set of rules. And remember that we have a bunch of rules there to whenever you have upward slopes, those air positive accelerations. So like here, when the slope is flat, you have zero acceleration. And then when it's downward, that's gonna be a negative acceleration. Also, the steeper you go. So if this is a one and a two, the more vertical you get, that's going to be higher magnitude or faster. Accelerations. So you could basically just copy exactly what you have for this table over here. Just move it down there. The same exact rules apply. So now let's go back to the question. We know we're looking for the acceleration. That's step one. Step two is which feature that's gonna be the slope, not the curvature. Be careful. Step three now is asking about the qualifier. So which qualifier makes the most sense? What we're talking about positive accelerations. And where does that happen for the slopes? That happens when you whenever you have upward slopes. So this happens when the slope is upward. So now let's just interpret that from the graph. Where do we have upward slopes just draw really quickly? All the slopes, it's gonna look like this like this. Here we go So where do we have upward slopes? That's gonna be a A B and G. So those are answers. Its's a simple Is that a B and G? All right, so now where's the boxes? Acceleration. Negative, guys. That the same list of steps again? We're just talking about the opposite thing. So we have the acceleration, Which means we're gonna talk about the slopes, which means qualifier. Now, what? We looked at positive accelerations, positive acceleration when we looked at upward slopes. So now it's just gonna be the opposite. Negative accelerations just means we're gonna be looking at downward slopes. So now where does that happen On the graph? Well, A and B up see us, flat, D and E or downwards. And the F and G are both flattering upwards. So that means we have d and E those air answer choices cool. Almost done here. So where is the box now? Accelerating the fastest. Okay, so we still have acceleration, so that's gonna be acceleration. We're gonna look at the slopes. So now which qualifier makes the most sense? Well, the other word that's important here is fastest. We've seen that before. Also fastest means like the most. Where is accelerating the most? Which qualifier makes the most sense from our list. It's gonna be the maximum. So, essentially, where is the maximum slope or what? Yeah, it was the steepest, almost vertical slope here on again. It doesn't talk about the direction. So this is a maximum. So we're gonna look at for the steepest. So where is the most vertical slope? Well, and be both look like that's B looks like this. And then e looks like it's a little bit steeper, a little bit more vertical like this. So that's actually gonna be at Point E. That's where it's accelerating the fastest and now last Now, last but not least, where is the box of speeding up? We've also seen this expression before. Speeding up means it is a change in your speed, not the speed itself. So we're still going to be talking about the acceleration. And so now we're still going to be looking at the slopes here. So now let's look at the qualifier. Well, remember that for position time graphs, there wasn't a very good qualifier that that dealt with Ah, speeding up because we had to look at the curvature of the graphs, and it's kind of similar here. There's not really a good qualifier, but we can do is kind of figure out a pattern for where you're speeding up. Speeding up just means that the magnitude of your velocity is getting higher. And we know that the magnitude of the velocity is just the value on the graph. The higher you go, the bigger than number. So one way you can think of speeding up is just any time you're going away from the time access. So any time you're going away from the time axis like this, for instance, at point B, that's gonna be where you're speeding up. And also, what happens is that point. You're also gonna go away from the time access, so this is gonna be speeding up, and then any time you're going towards the time axis like we are a point d, that's gonna be slowing down. Okay, so now where is the box gonna be speeding up? So we're gonna look for wherever we're going away. I point they were actually going towards the time access, so that's not right at point B. We're going away from it. So that's actually one of our answer choices. That's gonna be point B. C is flat. D is going towards So that's slowing down at e were at zero, but we're actually going to be increasing. So actually gonna be going away. So that's actually one of our answer choices as well. And then f is flat and then G is towards. So that's not right, either. All right, so those are two answer choices. It's just B and E. Alright, guys, let me know if you have any questions.