 Let's look at the difference between two very similar concepts, displacement and distance. When I talk about displacement, that's my change in position that I've been studying. Distance is just the total path traveled. Displacement is a vector because it matters which direction I go in when I change my position. The distance is a scalar, it only matters how far I went, not which direction. Because of this, displacements can be positive or negative and distances are always positive. Let's look at some examples. Most straightforward one. I've got a car traveling along a straight highway. It goes from mile marker 150 to mile marker 165. Even without drawing a diagram or writing out any equations, most people will very quickly realize that you travel the distance of 15 miles. The displacement is going to be a positive 15 miles. Again, these are the same quantities but since displacement matters which direction we're moving, we specify a positive or negative. And since we're moving forward from 150 to 165, we call that a positive displacement. One example, a ball rolls backwards from a position of 10 meters to a position of 4 meters. Here it may be helpful to actually put a number line up for ourselves just to kind of sketch it out. So our motion here goes from 10 meters to 4 meters, which as the problem says is the backward direction. Well, my distance is 6 meters. Just how far did I go, 1, 2, 3, 4, 5, 6 meters. My displacement is listed as the minus 6 meters because I'm going in the backwards direction. Here's another example. This one's a little more complicated. We've got a figure here that shows our positions of various objects along a number line. In this case, you're traveling from home to the bank and then to the library. My distance is 80 meters and I find this because I first went 60 meters from home to the bank and then went another 20 meters from the bank back to the library. My displacement though is just a positive 40 meters and that's because I ended up at a final position of the library, which is at 70 meters, and I started at home, which is 30 meters. So displacement only cares about where you ended up compared to where you started, your final position minus your initial position. It doesn't matter the path you took in between there. Here's a fourth example. We're using the same figure. In this case, we're going from home to school and then back to home. Our distance then is 60 meters. I went from home to school, which was 30 meters and then another 30 meters from school back to home. Displacement on the other hand is zero meters and that's because my final position, which was 30 meters, and my initial position, which was 30 meters, is the same thing. My displacement is telling me that over the course of this whole entire thing, I ended up back where I started from. I had no net displacement. The other way you can think about this one is the displacement on the first part of my trip was minus 30 meters. My displacement on the second part of the trip was plus 30 meters and so the two of those balanced out in the end to give us a net displacement of zero. You're going to see other examples of the difference between displacement and distance as we move through this physics course. Remember, displacement doesn't care what path you followed. It just cares about where did you end up compared to where you started. Distance does care about the path and it just is how far along that total path did you travel.