https://youtu.be/FGJ4DDe1k1w
PHYS 1101: Lecture Seven, Part Two
All right, where were we? Here’s my bird’s eye view of Section 2.7. The last thing we covered in Chapter 2 and that’s on graphing. It’s giving us a new way of visualizing this motion and helping understand motion.
We’re always going to be concerned with graphs, of our main vector quantities that describe the motion, the vector position, or the position coordinate, the velocity vector and the acceleration vector.
It’s always going to be, looking at these quantities versus time. It’s the time history of what that variable has undergone, and what happened to that part of the motion.
There is an important relationship between these three quantities: Position, velocity and acceleration. Let me remind you of that.
Velocity, by definition is a change in position divided by a change in time. Velocity tells us how the position changes with time. This I remind you is rise divided run, on a position versus time graph. Meaning if I go to the previous position versus time graph at t0 I had a certain position coordinate, x0, at a later time t. My graph tells me that x is now a position coordinate at a different value. So if I calculate the slope over this interval the number for that, the value for that… gives me that actual number on my velocity versus time graph. So, let me write here to emphasis that, so if you look at the slope on a position versus time plot, it gives you the actual value, or number on your velocity versus time graph.
For this particular scenario, the motion is a constant velocity. Meaning the position is just steadily increasing as time goes on. My slope over this whole range is constant, the value, the number of that slope will be the same constant velocity value for all times.
On the plot down below… let me emphasize the subsequent connection that we have.
The slope of this curve tells us about velocity and likewise the slope of the velocity curve tells us about acceleration. And that’s because the acceleration is v-v0 over t-t0. It’s the rise over the run of the velocity plot.
Acceleration tells us how velocity’s changing. So that would mean I take similarly two different time values and I ask how the velocity changes. For this middle example, there is zero acceleration. I see between two time intervals my velocity value hasn’t changed, the slope here is 0. That then matches my acceleration is 0 over that whole time interval. Again we can draw the same… so I can point out the same analogy I did before, mainly that the slope here gives me the value on the subsequent plot.
So let me write slope here leads to the value on the acceleration plot. The same trend applies to all these graphs.
Let me emphasize quickly down below. On my position plot now, when I have acceleration my position is increasing more and more as time goes on, but in any instance in time I can ask what is the slope at that instance. The slope would be the tangent line when I have a curve, and so the value of the slope, the rise over the run, would tell me at that same instance in time, it looks like it’s about 1, 2, 3 divisions over, at here, is time instant what the value is of my velocity.
So let me draw my arrow here and write “Slope equals this value”. From this plot to this plot, I have a velocity a graph, a straight line. The slope is the same anywhere along that line. So if I calculate that slope at that same time or in fact at any time my acceleration has the same constant value, which would be the value of this slope. So let me write “Slope gets me to the value.”
That’s really the best summary I can give you for graphing. You just have to become comfortable with it and practice is the best route to do that. Here again, I’ve repeated my main steps that I think will help you work your way through these graphs. The biggest piece of advice I can give you is slow down. People tend to make assumptions and jump ahead when they’re looking at these graphs.
Really first decide what is it that’s really being plotted. To get a good visual of what that motion means. Pick two time instances. Like I show you up here, pick two different time instances and really appreciated those time, read the graph, what is the value of those two time? What physically do these mean, and how is it changed? That’ll help you start to digest what the motion is and what the right picture is and what’s going on.
We’re now ready to move into our new material and that always starts with a reading quiz. So these were the sections you were given to read and I really focused on this last Section, 3.1 for these reading quiz questions. So here’s Question 2 for you, it’s again another symbol question, what physically is going to be represented or what variable symbol we’re going to physically represent displacement.
Question 3: In two dimensions, we’re going to use the textbook symbol. What’s v going to physically represent?