JASON HAFNER: All right. Our next example. Example two for kinematics is a smoothly rolling body beginning at the position Xi. So the subscript means the initial position Xi. And actually, we don't really want to do rolling. So we will eventually talk about rolling motion, very complicated. Right now, we just want to imagine the body just moving. So our demo is going to be Hal again. And the reason Hal is a nice shiny object is you can't tell that he's rolling. That's the idea. Now, Hal has been around a while, and getting some rust spots there. So I know how you feel. Trust me, I get it. So you might be able to tell that it's rolling, but just pretend that you can't tell that it's rolling. Because I can't afford another steel ball. They're kind of expensive. OK. So we're going to move just like that. There's your demo. So let's think. Hal started here. We'll call this Xi. We'll call this the origin, and there you go. Uniform motion. And it's not rolling. It is, we'll just say moving, and we'll ignore the rolling. OK. So we saw it. Now, let's first graph it. We're going to describe the motion with equations and graphs. So for the graph, we're going to do the same thing. It's going to be time on the horizontal axis. The X position on the vertical axis. We know that at time 0, we always put the origin here. 0, 0. We know at time 0, it started at Xi. So you'd plot it like this. You'd say, you know you started here. So at time equal 0, it was there. And then you can think, we're telling the story of Hal's motion, so we had one second, two seconds, three seconds, four seconds. And if we were to plot where it went, we know that in time from 0 to 1, it got a little bit higher. So I could put a mark there, a little bit farther along the x-axis. And in another second, it got a little bit further along the x-axis. And in the third second, it got a little bit farther. And after four seconds, it got a little bit further. And when we say smoothly, we kind of mean, more accurate might be uniformly. Might be a more descriptive word. So if it's moving uniformly, that basically just means it's going about the same amount of distance X in the same amount of time. That's what we mean by that. So if you have something that is uniformly moving, these points together make a line. So I could draw a nice line through those points. That is the kinematics graph for something moving uniformly. So the property we're going to talk about is that the body has velocity. Velocity. So if we had to define velocity, it is the rate of change of position with time. We're going to talk about several kinds of velocities, but that is the basic idea. It's how fast is the position changing in time. The symbol for velocity looks like this. Now, I don't know if you're going to know what that is. That is a cursive V. I know they don't teach cursive anymore. They used to teach us how to write in cursive. So if you don't know what weird symbol that is, that's my cursive V. I always use the cursive symbol when I'm talking about velocity. I use the regular symbol when I write the word. OK. Now, here's an example I can prove to you. This is one of my fourth grade cursive assignments. Look at that. It's beautiful. Look at that. Look how good I was at cursive in the fourth grade. Now, here's the grade. What! Give me a break. Oh, I was so mad about that. Destroyed my fourth grade GPA. But I don't hold grudges, so I'm completely over it. So this is the symbol, cursive V. The unit it's in meters per second. And we'll get more into the math of it in a minute. I just want to point out another thing. It is the slope-- if you've taken some algebra and done some plots and you know what slope is-- it is the slope of the x-t graph. And by that I mean the kinematics plot that you make or the graph you make when you put t on the horizontal axis like you always do, and you plot position on the vertical axis. Right. So if we were to take this line and find its slope, that would be equal to be V. OK. So now next, we'll move on and do this a little bit more mathematically.