### Measuring Motion

One step further and start measuring how far they go and what’s the first we require to measure how far they go? Something called a ‘scale’. So there have been primitive and old methods to do this. So we all keep one foot with us, we can walk around, here place one foot next to the other, next to the other, and so on. Count the number of footsteps you took. It’s a very simple way of measuring. What’s the problem with this? Each of us has different foot sizes and that becomes kind of a problem. And usually what they do is take the king’s foot and then they keep that as the foot. We all have this unit called foot, right? It was actually some old king’s, I think, I am not sure. So what happened was – you can do that, you can have one unit that’s that way or now you know that there are many more modern units that we have right now. Things like you know you keep one fixed measurement – we all agree that should be 1 meter or 1 foot or whatever it is. Then we can measure length that way. Length is a unit and that’s how we measure. A length is a quantity to measure what we call motion, right? So, somebody moved this much, right? And we say that ok, he moved, you know, some length. Let’s measure that length. And we measure it with a unit that we can talk about. Now, let us get one step deeper and let’s try to understand what this thing called distance is, because we keep talking about distance. Hey, how far is it, right? Of course, if you go and ask somebody in real life you know how far is something, they will tell you something like ‘its 15 minutes by train’. It’s a weird answer, isn’t it? You ask them how far and they give you an answer in time (which we will talk about again, what time really is – it’s really interesting). So what are we going to do now is let us say that you decide to go to your friend’s house. You know, it’s a party and you are here, and let’s say you are here and you know the route to your friend’s house somewhere there. Now obviously you can take more than one route to reach your friend’s house. So let’s say you are here and they are there. Awesome. So what you decide to do, you have an ice cream parlor there, so you want to take a route through that and go like this and reach there. Now what is the distance you have covered to reach your friend’s house? So if you have to find that out, you have to take a thread and put it on that road throughout, and then take that thread out and extend it, and measure how long it is, using any scale that you want. Your answer could be in centimeters, meters, you know this. So you have an answer. Is that the only path you could have taken? Of course not, right? You could have taken something else. Let’s say you will pick up a third friend and then go to that house. So you would go down somewhere here, pick your friend up and then start going up and reach your friend’s house. Now in this case you obviously, it looks like you covered a different distance. So you take a thread and measure the whole thing, stretch it out – different distance. So how many such distances are possible? Infinitely many, right? Assuming that there are enough roads and to whatever path you want to take, you could have taken any number of paths. So all those correspond to different distances. Of all these distances, one of them is very special. If you were to take that shortest path between these two, what would that be? Between any two points, we know what is the shortest path, right? As long as they are on a plane, the shortest path is going to be a straight line that connects them, and why am I saying this? If it is on the Earth, this is not true. Rigorously, right? Because the Earth is kind of a sphere. The shortest distance between this and that in reality would be this, but if you are on Earth, you will probably have to walk around there and go there, right? So, forgetting that, assuming all distances are quite small and the Earth can be assumed to be flat, right, because we are walking from here to another point, you are probably not going from the North Pole to the South Pole, or something like that. So assuming its flat, it’s going to be the straight line that connects them, and that straight line, between these two points is going to be called the displacement. Because sometimes you don’t care about the actual path you took, but you only care about where you began and where you end. That’s all you care about. So there are two quantities that we’ve spoken about. We are going to expand about them in a while, but the quantity one is distance, which is the length of the actual path that you took between two points, A and B. So you take some path, put a string through them, take that string out, stretch it out and measure it. And this other quantity, which does not care about which path you actually took but only cares about the starting point and the ending point and calculates the shortest distance between them the two of them.