 Okay, here is a really basic velocity position question. I'm just going to make something up, just off the complete top of my head. Okay, so let's say we have R2D2, you know, and he can fly, right? And let's say that here is the origin, and so at some time T1, he is at position R1, and then later he's over here at position R2 at time T2, okay, so he, because he can fly. He could always fly, just so you know, he could always fly. He just chose not to fly when it was very convenient later, but that's R2D2's problem. That's not our problem. We're doing velocity. Okay, so let's just make up some stuff here. Let's say that R1 is 1, 4, negative 3 meters, R2 is 8, 1, negative 2 meters, I mean, so this is the x-axis, and this is the z-axis, and so this is positive z, so that's negative z, so he's kind of behind the board. Okay, so maybe that's where the camera is. And let's say T1 is 1.5 seconds, and T2 is 6.2 seconds, and it doesn't really matter what he did. He may have gone like this. You know R2D2 kind of flies weird sometimes. It doesn't matter, but we want to calculate his average velocity, the average velocity during this time. So I can say V average, the definition of average velocity, change in position over change in time. That's it. So what was the change in position? Well, whenever you change in position, it's final minus initial, so it's going to be this vector, I'll call it delta R. So delta R is R2, not R2D2. This is lowercase R, just R, R2 minus R1. And then delta T is going to be T2 minus T1, so that's going to be 3.7, 3, no, 4, y, y, okay, let me switch these up. And when you're doing something at the board, sometimes you just feel dumb, okay. So this is going to be 5.3. Now all I need to do is calculate delta R. Delta R is going to be R2 minus R1, so it's 8 minus 1, 7, 1 minus 3, negative, 1 minus 4 is negative 3. And then negative 2 minus negative 3 is going to be 1. So now I can calculate the average velocity. It's going to be this delta R divided by that delta T, so I can write that as, you know, this may not show up in the video. Let me write it up here. I don't like to go out of order, but the average is going to be 7, 7 over 5.3, negative 3 over 5.3, 1 over 5.3. And these have, you know, some meters over seconds, this is meters per second, and that's my average velocity. That's the average velocity. Now you know, if I let the time interval go really, really small, then there's really not going to be a difference between the average and the instantaneous velocity. And the other thing that we could do is with this, and sometimes we know the average velocity and we want to find out where the thing is. I didn't do that problem, but if I had, let's say I knew where R1 was and I knew V, average, but I didn't know R2, then I could say this is R2 minus R1 over delta T, and then I can just solve for R2. R2 is going to be multiplied by delta T and then add R1, so I get R1 plus V average delta T. Now this doesn't matter if delta T is big or small. All that it matters is that we use the average velocity, okay? Now and that's the thing, sometimes the average velocity is very close to the instantaneous velocity. Okay, that's it.