 Hi, I'm Zor. Welcome to Unizor education. This lecture is the first one in mechanics part of the physics for teens course presented on Unizor.com website. If you found this lecture anywhere else like on YouTube, for instance, I do suggest you actually to go to Unizor.com to physics for teens section and you will find the same lectures. But in addition on the website you have certain functionality built into it. You have notes for each lecture and you will have exams. The site is free, has no advertising, so there are many advantages and no disadvantages to use Unizor.com as the base for your studying. So this is the first lecture and the first lecture is dedicated to a concept of motion. Okay, so we are talking about motion. Obviously, when we are talking about mechanics, especially the first part of the mechanics, which is called kinematics, which basically studies the motion. There are no forces yet involved. Just pure motion. We have to talk about how things are moving. Okay, now when we are talking about moving, we have to talk about two things. Number one, what is moving and number two what basically the moving itself encounters, what it represents and how can we describe it. So the object and its movement. Well, the object which we will consider most frequently in this course, which is moving, is basically a mathematical point. Yes, I understand that there are different objects. There are cars and there are blocks or something else which are moving and we will probably resort to certain words which describe them. However, in all these cases or in most of these cases, we will consider the car as a point actually, which is moving in certain direction or a rocket or something else. So whenever we are talking about movement, right now and in most other cases in the future, we will talk about movement of the point where in the space obviously. Now, what is the space? Space is our three-dimensional space, which we know about. So basically these two characteristics, the point and a three-dimensional space where it exists defined the object. Now, what is the movement? Well, it's a movement of the point, right? So basically we have to somehow study how the point moves in space. Okay, that's fine. Now, these are kind of qualitative characteristics. The second thing which we must actually do is to go to a quantitative characteristics. All right. So what is the quantitative characteristic of a point? Well, point has no dimensions, right? So it's basically, well, a point and point is not defined by mathematicians. It's undefined concept as unfortunately many others and we don't have any other choice but to basically say that this is undefined. So point is point has zero dimension in any direction and that's basically all the quantitative characteristics we can suggest. Now, talking about movement within the space, well, we have to really have coordinates in this space, right? And then we can actually quantify what movement actually is. When the point has some coordinates at one particular moment in time and other coordinates in another moment of time. Okay, so these are quantitative characteristics of the movement. But now I have used another very interesting concept, the concept of time. Also, by the way, undefined, unfortunately. However, we can measure it. We can, well, time actually is our view until any process. So all the processes which are happening in this universe, they are actually, they are occurring in time and we can measure the progress of one process relative to another. And actually that's how we can establish the unit of time. Like, for example, we can say that one rotation of the Earth, the planet, around its axis is 24 hours and every hour is 60 minutes and every minute is 60 seconds. And that's basically how we introduce a unit of measurement. So one second would be one second. It's 186400 of rotation of the Earth around the its own axis. I mean, there are other equivalent measures, maybe much more precise. But for our purposes, all we need to basically say is that we can measure time and time is a very important characteristic of every movement because whenever we are saying that the point changed the position in time, we actually have to understand what time is and we have to measure the time as much as we can measure change in the position. So changing the position is kind of more easy, if you wish, because this is basically the length. Now, if we have a system of coordinates x, y and z, now the point has certain height, certain coordinates along the x-axis, along the y-axis. Now, this is my x-coordinate, this is my y-coordinate and and something like this. And this is my z-coordinate, right? So we know how to measure the position and we know how to measure time. Now, that's basically sufficient to describe the motion as some kind of a function of the position of time. So the position would be our value of the function and time would be an argument. The only thing is we really have to say whenever we are talking about time, we have to know where is the beginning of time and what's the unit of time. Okay, unit of time, for instance, is a second. We have already established that. And by the way, the second is a standard for international research in physics. Now, as far as the beginning of time, well, we don't really know what's the proper beginning of time anyway. Now, traditionally, if we are talking about movement, the beginning of time is usually, at least in all practical sense, is the beginning of the movement. So whenever we are saying, okay, at certain moment of time an object starts moving, well, that particular starting time, we can always say this is the time zero. This is t equal to zero. Initial moment, initial start of the movement. I mean, there might be some other cases. It depends on the task at hand. However, it's reasonable to assume that whenever the object starts moving, we are saying, okay, beginning of time is the moment it starts. Great. Now, how about position? Again, we do have measures of the lengths on each axis. Usually, we are using, in international standards, its meter, which is the standard, as the lengths. Everything else, obviously, can be derived from the meter, millimeter, kilometer, even inches and miles, et cetera. So let's use the meter as a unit. But again, where is the origin of coordinate and what's the directions of the axis? Well, again, it's basically up to us, because if we are describing something, we are describing by establishing what is the origin of the coordinate, where are the directions of the axis, and what is the beginning of the time. And again, the most convenient way in many cases, in many practical cases, to use as the origin of coordinate the point exactly where the movement starts. Now, as far as the direction of the axis, well, it depends again. In most of the cases where we know that the object is moving along the straight line, we will usually put the x-axis along that direction, in which case y and z will always be equal to zero, because the object will be moving along the x-axis. That's the most convenient kind of way in many cases. And obviously, we will use it. And there are obviously different cases. For instance, if the object is circulating around some center, then obviously, we will use the x-y plane within the plane of the movement, and z would be perpendicular to it, and it will always be equal to zero. So that's also kind of convenient. So it's up to us, but we do have to choose the origin of coordinate. We have to choose the direction of the axis, and we have to choose the moment where we start counting the time. Now, the units are already established, a second for the time, and a meter for each axis of the coordinates. Now, if we have done what I was just suggesting, can put the origin of coordinate exactly to the point where the movement starts, then we can say that our functions of coordinates as functions of time are such that at moment zero, they all are equal to zero. Because at moment zero, we have chosen that's where the start of the movement actually is located, and we have that this is the origin of coordinate. So at moment zero, we are in the origin of coordinate, and then the movement starts. This is one of the convenient cases. Now, so how to describe the motion? Well, the motion is described by these three functions, which exist in our established system of Cartesian coordinates with certain moment in time chosen as the beginning of the time. And obviously, the units of measuring, units of measurements of the lengths to know the position and the time to know the time are established and well standardized. In this case, and in many others, I will use the second for the time and the meter for the lengths because these are international standards. So basically, all I'm saying is that these three functions together with the system of coordinates and the beginning of time that we have kind of established or agreed upon, these are the quantitative characteristics of any motion. And that's the result of this, basically, discussion which I wanted to provide today. This is something which is the most important point. These three functions are defining the motion within the system of coordinates and within the time frame. That's it for today. Thank you very much and good luck.