 We've been describing motion using our normal everyday language throughout our whole lives. In physics we sometimes have to be a little bit more careful, so let's just take a few moments to recap some of the concepts we've introduced and look carefully at their definitions. So we normally describe motion in the real world in three dimensions, and that's a little bit tricky, so for this discussion we'll just talk about travelling along in a particular straight line. And as Vanessa's already discussed, what we need to do in order to describe that we need to be able to say where things are, so we need some kind of coordinates, so we have a zero in position, and then if we're at a particular position up here, we say that we are a distance x from that origin, and that position might change over time if we're moving around. So one of the things we have to be careful about to distinguish in physics is the difference between displacement and distance. Supposing I started at the origin and I travelled all the way over here, and then turned around and came all the way back to here, and so I ended up at that point there. Now if I'm there, the question you might ask is how far did I travel? And there are two perfectly reasonable answers to that. One answer says, well, I travelled that amount of distance, and then I travelled this bit back, and so I have to add that together, so I add those together, and that's how far I travelled. Another perfectly reasonable answer is, well, I only got that far. So that's how far I travelled. And those two answers are given different names in physics. The one where we have the long trip is called the distance you travelled, and this difference between where you started and where you ended is called the displacement. When we start worrying about directions of things again, we'll notice that distance doesn't have a direction. Distance is a scalar quantity, whereas displacement does care about direction. If I'm there, that is a different displacement to there, and so displacement has direction, and when we're just on a line, it can only be positive or negative, but that means it's a vector quantity. We can talk more about how to deal with vectors that aren't all in one line later. Now if we want to talk about something moving around in time, a good way to describe that is with a graph. And so if we have a graph of position as a function of time, then if they're not moving at all, they'll stay at the same position. And if they are moving, this will have a slope, and if they change the slope, that means they're going to change their velocity. And it turns out that in physics we make a distinction between speed and velocity, and it's exactly the same distinction we're making up here. So the speed is just the total distance travelled divided by the time taken. And so that's a scalar property, just like distance was a scalar property. So if you jump out of a car and you go onto the highway and go as fast as you can to the nearest city, then you turn around and come almost all the way back again, then your speed can be extremely high, because you travelled a very large distance in a fairly short time. But your displacement was quite small, because you ended up almost back where you started from, and so that means your velocity is low. So velocity is a vector, because it's got a direction. So if you travel backwards, then you have a negative velocity. So the velocity here would be zero, the velocity here would be positive, because x is getting bigger over time, and the velocity here would be negative, because x is getting smaller over time. We've already spoken about the difference between instantaneous and average properties. And so if we look at a very small piece of time, of time delta t, then a particle moves a distance delta x, and our instantaneous velocity is going to be just that delta x over delta t. So while you might use the formula that the velocity is a change in position over a change in time, it comes up in a lot of different contexts. You have to make sure whether you're talking about things like average velocity or the instantaneous velocity. And of course, most commonly, the velocity is changing over time. Or there might be more than one thing, so there's more than one velocity. So whenever you're dealing with a real problem, make sure that you draw a diagram and make sure that you write the particular symbols you're talking about, and you're very clear, and use words to describe what you're talking about when you talk about these symbols. And the situation where the velocity is changing is where there's an acceleration. And just as the velocity is the rate of change of displacement, the acceleration is the rate of change of velocity. Now, acceleration doesn't have a scalar version because by the time you're talking acceleration, you're normally talking to a physicist, in which case you're normally talking about the vector quantity first time. However, we do use acceleration in day-to-day life. For example, you might say, I'm going to jump in my car and I'm going to accelerate. So I press the accelerator, and that makes me go faster. And people are happy that that means acceleration. But what happens when I press the brake? That slows me down. Well, to a physicist, that's still acceleration. Because you're still changing your velocity, you're just changing it with a negative sign. And so you're accelerating backwards. So acceleration is a vector quantity. Another example of acceleration that typically is not understood as acceleration is where you're changing direction. Supposing you're in a car and you go around a corner, even if your speed says exactly the same, people might say that therefore you don't accelerate because you're not going faster or slower. But because your velocity is changing, because remember velocity has direction in it as well, that means you must be accelerating. So something has to happen in order for you to change that direction. And you'll find that very clearly if you try and turn a corner in a car and the road is very icy. If you don't have friction with the road, you don't get to change your velocity. And once again, of course, you can talk about an instantaneous acceleration or an average acceleration, exactly the same sense as you do for velocity. An instantaneous acceleration is the acceleration defined over a short period of time. And an average acceleration is the acceleration defined over some large period of time.