Basic concepts of kinematics and equations

What are the basic concepts of kinematics? What kind of science is this and what does she study? Today we will talk about what kinematics is, what basic concepts of kinematics take place in tasks and what they mean. In addition, let's talk about the values that are most often dealt with.

Kinematics. Basic concepts and definitions

First, let's talk about what it is. One of the most studied sections of physics in the school course is mechanics. Molecular physics, electricity, optics and some other sections, such as, for example, nuclear and atomic physics follow in an indefinite order. But let's take a closer look at the mechanics. This section of physics deals with the study of the mechanical motion of bodies. It establishes certain regularities and studies its methods.

Kinematics as part of mechanics

The latter is divided into three parts: kinematics, dynamics and statics. These three sub-sciences, if they can be called so, have some peculiarities. For example, statics studies the rules of equilibrium of mechanical systems. Immediately comes to mind the association with the scales. Dynamics studies the patterns of motion of bodies, but at the same time draws attention to the forces acting on them. But the kinematics is engaged in the same, only in the account of force are not accepted. Consequently, the mass of the same bodies is not taken into account in problems.

Basic concepts of kinematics. Mechanical movement

The subject in this science is the material point. It means a body whose dimensions, in comparison with a certain mechanical system, can be neglected. This so-called idealized body, akin to an ideal gas, which is considered in the section of molecular physics. In general, the concept of a material point, both in mechanics in general, and in kinematics in particular, plays a rather important role. The so-called progressive motion is most often considered .

What does this mean and how can it be?

Usually the movements are divided into rotational and translational. The basic concepts of the kinematics of translational motion are associated mainly with the quantities used in the formulas. About them we'll talk later, but for now let's return to the type of movement. It is clear that if we are talking about rotational, then the body is spinning. Accordingly, translational motion will be referred to as moving the body in a plane or linearly.

Theoretical basis for solving problems

Kinematics, the basic concepts and formulas of which we are considering now, has a huge number of problems. This is achieved through the usual combinatorics. One of the methods of diversity here is changing the unknown conditions. One and the same problem can be represented in a different light, simply changing the purpose of its solution. It is required to find the distance, speed, time, acceleration. As you can see, the options are the whole sea. If we connect the conditions of free fall here, the space becomes simply unimaginable.

Values and formulas

First of all, let us make one reservation. As is known, quantities can have a twofold nature. On the one hand, a particular value may correspond to a particular numerical value. But on the other hand, it can have a direction of distribution. For example, a wave. In optics we are faced with such a notion as the wavelength. But if there is a coherent light source (the same laser), then we are dealing with a beam of plane-polarized waves. Thus, not only the numerical value, indicating its length, but also the given direction of propagation will correspond to the wave.

A classic example

Such cases are an analogy in mechanics. Let's say we have a cart before us. By the nature of the motion, we can determine the vector characteristics of its velocity and acceleration. To do this in a forward motion (for example, on a flat floor) will be a little more difficult, so we will consider two cases: when the cart rolls up and when it slides down.

So, let's imagine that the trolley is going up a small slope. In this case, it will slow down if external forces do not act on it. But in the reverse situation, namely, when the trolley slides down from above, it will accelerate. The speed in two cases is directed to where the object is moving. This should be taken as a rule. But the acceleration can change the vector. When decelerating, it is directed to the opposite side for the velocity vector. This explains the slowdown. A similar logical chain can be applied to the second situation.

The remaining values

We have just talked about the fact that in kinematics we operate not only with scalar quantities, but also with vector quantities. Now we will take one more step forward. In addition to speed and acceleration in solving problems, such characteristics as distance and time are applied. By the way, the speed is divided into the initial and instant. The first of these is a special case of the second. Instantaneous speed is the speed that can be found at any time. And with the initial, probably, everything is clear.

A task

A considerable part of the theory was studied by us earlier in the preceding paragraphs. Now it remains only to give the basic formulas. But we will do even better: we will not just consider the formulas, but we will also apply them in solving the problem in order to finally consolidate the knowledge gained. In kinematics, a whole set of formulas is used, combining which, you can achieve everything you need to solve. We give the problem with two conditions in order to understand this completely.

The cyclist brakes after crossing the finish line. For a complete stop, it took him five seconds. Find out with what acceleration he braked, and also what braking distance he managed to pass. The brake path is assumed to be linear, and the final speed is assumed to be zero. At the time of crossing the finish line, the speed was 4 meters per second.

In fact, the task is quite interesting and not as simple as it might seem at first glance. If we try to take the distance formula in kinematics (S = Vot + (-) (at ^ 2/2)), then nothing will come of it, since we will have an equation with two variables. How to act in this case? We can go in two ways: first calculate the acceleration by substituting the data in the formula V = Vo - at or express from there the acceleration and substitute it in the distance formula. Let's use the first method.

So, the final velocity is zero. The initial - 4 meters per second. By transferring the corresponding quantities to the left and right sides of the equation, we obtain the expression for the acceleration. Here it is: a = Vo / t. Thus, it will be equal to 0.8 meters per second in a square and will carry a braking character.

Let's go to the distance formula. In it we simply substitute the data. Get the answer: braking distance is 10 meters.