https://youtu.be/2qwgz3OPjEU
PHYS 1101: Lecture Six, Part Five
Okay. Let’s just practice, practice, practice now. Go through several examples, and we’re going to make these quiz questions, and I’m going to help you through the first ones as we start.
One of the first tricks I want to point out is perhaps something you can sketch along your graph to help you picture the motion. I’m going to make this a little bit smaller, so I have room. We’re used to looking at these motion diagrams now. Usually, for x, for example, we’re looking at that horizontal motion. So, imagine that you turn your page. If you printed out your notes, do a rough sketch of this graph, and then rotate your page so that this line is horizontal.
When that line is horizontal, then above this, I’m going to think of sketching in my motion diagram for that object. Well, what do I know? What do I know? At the initial time, the object was at +2 meters. At the initial time, here’s my origin, the object is here. Then, I know one second later, it’s moved to the next position, 3. Another second later, it’s moved to 4. Another second, looks like it’s about up to 5.
Well, then what happens? In the next second, it now goes back to near the origin. It’s now heading back toward the origin, and it looks like in the next second, I travel pretty far. I travel 1, 2, 3 meters. So, in the next second, let me just repeat this point right up here, so I double back on myself. In the next second, I travel all the way back to this point.
Looks like for the next second, I stand there. So, that would be another point there. Now, I continue heading back to the origin. In fact, I continue heading now in the direction of negative x values.
So, if I go in and add some velocity vectors between my motion diagram, it really helps me to tie this plot to more of a visual picture of what that object is doing. If I do that, I think it’s a lot easier than to answer these questions. So, given this motion diagram, I started here. Here was t equals 0. I did something like this. I’ve even been able to convey the rough size of the velocity at different intervals. Does that object ever turn around? And if so, when?
Okay. Next question. You’re looking at the same plot. Here, it’s asking you about the velocity, and is the velocity ever negative. Well, if you’ve gone through that exercise to do a quick motion diagram, you could go back and look at these velocity vectors, and you could say to yourself, “Okay. A negative velocity means that this vector has to point in the negative direction. And you know what? It does point in the negative direction for part of this motion. Let’s see. When did that start? That started here, after the first three seconds when the object turned around.”
Another way to recognize the sign of velocity is just to think about the slope again. You glance at this plot, x versus time, and you look at the slope of these segments. It’s telling you the velocity. This is a positive slope, positive velocity. The slope here, negative, velocity in the negative direction, etc. Okay. So, that should help you with Question 7.
Okay, question 8, at first, appears to be a question that we’ve already answered. But, here’s where I ask you to slow down. This is a plot now of velocity versus time. To help orient yourself to this, I might just suggest that you start out drawing some velocity vectors, this is velocity versus time, to then help you somewhat picture what’s going on.
The first velocity vector I need to draw is kind of small, has a length of about 2 meters per second, but it’s positive. Let’s make that represent 2 meters per second. The next second later, the velocity has increased to 3 meters per second. As time continues on, it increases further and further. At this highest point, the velocity, note it’s still positive. We’re still above the origin. It’s just getting smaller. Velocity keeps getting slower.
Eventually, it gets even less than, looks like it’s starting less than where we started, so slightly shorter than where we started. And now, the velocity keeps getting smaller, goes to 0. Now, the graph is telling me that for these times . . . Let me highlight that in orange maybe. For example, at this time, my curve is below the line. That means my velocity is now in the negative region. So, on my plot, that means my velocity did this. It eventually went to 0, and then it flipped sign. Okay. That might help you there.
Question 9. Does the object ever stand still? And if so, during what segment? Again, slow down. We’re back to thinking about x versus time. Go back or do your motion diagram here, and see if you can then answer this question.
Okay, question 10. When is the object going the fastest? You’re asked that question, and you’re looking at the direct velocity versus time. Remember the value of velocity. That is a number that represents how fast you’re going. When is it going the fastest?
Question 11. You have two objects here. You’re looking at the plot of the position versus time for these two objects. You’re asked about the speed. Remember, speed is the magnitude of velocity. How is velocity related to a plot of x versus t? You got to think slow. I’ll leave that to you to answer that one now.
Alright. I want you to now try to go in the other direction, and I don’t know how to ask you to practice this other than what I’ve done here. You now have some practice of looking at a graph and reading the graph and trying to interpret what the motion looks like. Can you go the other direction? If I describe some motion to you, can you generate a graph that represents that motion?
So, read this discussion here, this description of motion, and then generate that graph on a piece of paper. I can’t think of a good way of having you submit that to me electronically, unless all of you have scanners, which you may not. The next best thing is to ask you to, using text, to just describe that graph to me in words. Be as specific as you can. You’re looking at your graph. Tell me what direction your axes are, what numbers are at various positions on your graph, and what does your line look like that you’ve drawn on your graph. Be as specific as you can.
Okay. To again further your skill in being able to graph something, given the physical description, for the same motion, now instead of graphing x versus t, graph the velocity versus time for me, for that object, for that four-second interval. Describe that graph, and again, be as specific as you can.
Okay. The last three questions here have to do with getting a feeling for acceleration and how you can look at a graph and say something about the object, whether the object is speeding up or slowing down. You’ve got four questions to ask about that, to answer about that. The only reminder I’m going to give you is that the acceleration is v minus v0 over Δt. It’s the slope on a v versus t curve.