SPEAKER 1: Now, we're going to talk about 2D kinematics. My simple definition of 2D kinematics is keeping up with x and y motion. It's really not that different from 1D kinematics. We just now have two dimensions to keep up with. Our demo of 2D kinematics is to have a ball roll on a 2D plane, and then we'll plot it and do the equations, like we always do. Now, Hal was supposed to do this, but Hal's a little bit of a prima donna. He said something about rust marks starting to show up, and he kind of freaked out. So, this is one of the plastics, who you're going to meet later, is going to do it. The plastic is going to start at a little bit of an offset, on the y-axis, and then, just kind of go like this in a nice, uniform, smooth motion. Let's make a plot of that here. So, plus y, plus x. This is not a kinematics plot. This is a trajectory plot. And remember, started out a little bit up on the y-axis and moved kind of like that. That's the actual path that the ball took in x and y. Something like that. So, if we were to catch it at snapshots in time, something like this. Equal displacements with equal amounts of time. How do we treat the kinematics? What do we do? It's very simple. You treat x and y separately. There we go. Treat x and y separately. Since they're not coupled, since the x position doesn't affect the y motion, and since the y position doesn't affect the x motion, it's like two separate motions happening at the same time. So, if we wanted to, we could even do the kinematics completely separate. We could make a plot of the y versus time, and we can make a plot of the x versus time. Let's see-- y had a little bit of an offset and went at some slope. X, we start at the origin, but the slope was actually higher. I kind of had it moving a little faster in x than I did in y. That would be a reasonable plot. Since it was a constant velocity, we could do constant velocity kinematics. If we wanted to, we could say, well, y final equals y initial plus vyt. We could keep up with where it is on the y-axis at all times. And, we could say x final equals-- actually, there is no x initial, so I'll leave that out, right? This one had a y initial, and this one doesn't. So, x final equals vxt. You could do them completely separate. And that's one way you can do it, but actually, on the next board, I'm going to show you how to do it a little bit more sophisticated. It's actually better to keep it all together, so I'll show you that next. But, in principle, it's just two separate motions.