Kinematics is ... Kinematics: definition, formulas, tasks

What is kinematics? This is a subsection of mechanics, which studies mathematical and geometric methods of describing the motion of idealized objects. They fall into several categories. The topic of today's article will be aspects that are somehow related to the concept of "point kinematics". We will deal with many issues, but we will begin with the most fundamental concepts and explanations for their application in this field.

What objects are considered?

If kinematics is a branch of physics that studies ways of describing the motion of bodies in disparate spaces, then you need to operate on the bodies themselves, right? To quickly understand what is at stake, you can find a multimedia lesson for school students. Kinematics for understanding in general is simple, if you understand its fundamentals. When you become acquainted with them, you will notice that in theory there is information that this section of physics is studying the laws of motion of material points. Notice how the definition of objects is generalized. On the other hand, material points are not the only objects considered kinematics. This section of physics studies the principles of motion of absolutely rigid bodies, and ideal liquids. Very often all these three concepts are combined into one, simply "idealized objects". Idealization in this case is necessary for the conventions of calculations and a departure from possible systematic errors. If you look at the definition of a material point, you will notice that the following is written about it: this body, whose dimensions can be neglected in the appropriate situation. This can be understood as follows: in comparison with the distance traveled, the linear dimensions of the object are negligible.

What is used to describe?

As it was said before, kinematics is a subsection of mechanics, which studies ways of describing the motion of a point. But if this is so, then for the commission of such operations, some fundamental concepts and principles are needed, like axiomatic ones? Yes. And in our case they are. First, in kinematics, it is usually the rule to solve problems without looking back at the forces acting on the material point. We all know perfectly well that the body will be accelerated or slowed down if a certain force acts on it. And kinematics - this is the subsection that allows you to operate with acceleration. However, the nature of the arising forces is not considered here. To describe the motion, methods of mathematical analysis, linear and spatial geometry, and also algebra are used. A certain role is played by coordinate grids and coordinates themselves. But we'll talk about this a little later.

History of creation

The first works on kinematics were compiled by the great scholar Aristotle. It was he who formed some fundamental principles of this industry. And even though his works and conclusions contained a number of erroneous opinions and reflections, his works are still of great value for modern physics. The work of Aristotle later studied Galileo Galilei. He conducted famous experiments with the Leaning Tower of Pisa, when he studied the laws of the process of free fall of the body. After studying all the length and breadth, Galileo subjected Aristotle's reflections and conclusions to harsh criticism. For example, if the latter wrote that force is the cause of the movement, Galileo proved that force is the cause of acceleration, but not what the body will take and will move and will move. According to Aristotle, the body could acquire speed only under the influence of a certain force. But we know that this opinion is erroneous, because there is a uniform progressive movement. This once again proves the kinematics formulas. And we will proceed to the next question.

Kinematics. Physics. Basic concepts

In this section, there are a number of fundamental principles and definitions. Let's start, perhaps, with the main one.

Mechanical movement

Probably, from the school bench we are trying to lay the idea of what can be considered a mechanical movement. We face it every day, every hour, every second. By mechanical movement we will consider the process that takes place in space over time, namely the change in the position of a particular body. In this very often relativity is applied to the process, that is, it is said that the position of, say, the first body has changed with respect to the position of the second. Let's imagine that we have two cars on the starting line. Operator's signal or the lights caught fire - and the cars break off. At the very beginning, the situation is changing. And you can talk about this long and tedious: with respect to the competitor, with respect to the start line, with respect to the fixed viewer. But, probably, the idea is clear. The same can be said about two people who go either one way or different. The position of each of them relative to the other changes at each moment of time.

Reference system

Kinematics, physics - all these sciences use such a fundamental concept as frames of reference. In fact, it has a very important role and is practically applied in practical tasks almost everywhere. Two more important components can be associated with the reference frame.

Coordinate grid and coordinates

The latter are nothing more than a set of numbers and letters. Using certain logical settings, we can compose our one-dimensional or two-dimensional grid, which will allow us to solve the simplest tasks of changing the position of a material point for a particular period of time. Usually in practice, a two-dimensional grid is used with the axes X ("x") and Y ("yerk"). In the three-dimensional space adds the Z-axis ("ZET") and only X is present in the one- dimensional space . Artillerymen and scouts often work with coordinates. And for the first time we come across them in primary school, when we begin to draw lengths of a certain length. After all, graduation is nothing more than the use of coordinates to indicate the beginning and end.

Kinematics 10 class. The values

The main quantities that are used to solve problems in the kinematics of a material point are distance, time, speed and acceleration. Let's talk about the last two in more detail. Both these quantities are vector. In other words, they have not only a numerical index, but also a certain given direction. The motion of the body will occur in the direction in which the velocity vector is directed. In this case, we should not forget about the acceleration vector, if we have a case of uneven motion. Acceleration can be directed in the same direction, or in the opposite direction. If they are co-directional, the body will move faster and faster. If differently directed, the object will slow down until it stops. After this, in the presence of acceleration, the body will gain the opposite speed, that is, it will move in the opposite direction. All this in practice very very clearly shows the kinematics. The 10th grade is just the period when this section of physics is being revealed to a sufficient extent.

Formulas

The kinematics formulas are quite simple both for output and for memorization. For example, the formula of the distance traveled for a particular time has the following form: S = VoT + aT ^ 2/2. As we see, on the left side we have just the distance. On the right side you can find the initial speed, time and acceleration. The plus sign is purely arbitrary, since acceleration can take a negative scalar value when the object brakes. In general, the kinematics of motion implies the existence of one kind of speed, we constantly say "initial", "final", "instantaneous". Instantaneous speed appears at a certain point in time. But if you think about it, the final or initial components are nothing more than its particular manifestations, right? The theme "Kinematics" is, probably, a favorite among schoolchildren, since it is simple and interesting.

Examples of tasks

In the simplest kinematics, there are whole categories of very different tasks. All of them are somehow connected with the motion of a material point. For example, in some it is required to determine the distance traveled by the body in a certain time. In this case, parameters such as initial velocity and acceleration can be known. And maybe the student will be given a task that just the same will consist in the need to express and calculate the acceleration of the body. Let us examine an example. The car starts from a static position. Which way will it pass in 5 seconds if its acceleration is equal to three meters divided by a second in a square?

To solve this problem we need the formula S = VoT + at ^ 2/2. In it, we just substitute the available data. This acceleration and time. One should pay attention to the fact that the term Vot goes to zero, since the initial velocity is zero. Thus, we get a numerical response of 75 meters. That's all, the problem is solved.

Results

Thus, we understood fundamental principles and definitions, gave an example of a formula, and talked about the history of the creation of this subsection. Kinematics, the concept of which is introduced in the seventh grade at the lessons of physics, continues to be constantly improved within the framework of the relativistic (nonclassical) division.