The concept of speed is one of the key in characterizing the dynamic parameters of both an individual object and some system. Indeed, speed is the most important physical quantity that characterizes movement, and a person constantly encounters the concept of movement in his life. And no matter, this refers to the movement of molecules or multi-ton trucks, pedestrians or multi-meter trains. That is why the study of speed as a physical quantity in the school course of mathematics and physics takes a lot of time, and such attention is paid to this parameter not only with the fact that a person is constantly faced with movement, but also with the fact that the concept of speed is diverse.
The first tasks on how to find speed, students meet in the mathematics course of elementary school (as a rule, these are grades 3 and 4). These tasks, of course, are elementary and are devoted to the consideration of an ideal model of mechanical motion. Students begin to get acquainted with the mathematical description of the movement of bodies with the most important concepts - path, speed and time - and the well-known formula that states that the path is the product of the speed of movement and the time of movement.
At the same stage, in the school course, mathematicians consider the concept of productivity, telling students how to find the speed of work. This approach is very appropriate, because the mathematical descriptions of these processes are similar, and therefore, it will be easier for students to understand the meaning at first glance of very complex definitions of work and productivity.
After mastering the elementary laws of mechanical motion on the example of one body, students become acquainted with the phenomenon of movement of several bodies at the same time. Of course, in elementary school, the consideration of this process takes place on elementary examples and ideal models. Students solve problems and learn how to find the speed of approach, if one body catches up with another or two bodies move towards each other.
Problems dedicated to speed continue to be encountered by students and middle-level school mathematics students. In the fifth grade, students become familiar with the concept of average speed. It is very important to emphasize that the average speed and the arithmetic mean are different values. Often, students confuse these concepts by projecting a formula for calculating the arithmetic mean on problems devoted to motion. It is important to explain how to find the speed if the movement is made in different, different from each other time intervals with different speeds.
More complex phenomena of mechanical motion are considered in the school physics course, which begins to be studied by students in the 7th grade. At first, elementary concepts of motion are also considered here, related to questions of how to find the initial velocity of a body before acceleration, or how to calculate the path traveled by a body to a specific point in time.
In the 9th grade, students get acquainted with the concept of movement and its difference from the path. At the same stage of studying mechanical motion, students are introduced to the solutions of classical problems on how to find the speed of approach of bodies moving at an angle to each other and, in particular, perpendicularly.
The course of mechanics continues at the senior level of the school course in physics, but here the emphasis is on solving problems associated with the movement of many bodies or with complex movements of one body. For example, in the 10th grade a lot of time is devoted to tasks devoted to the movement of the body at an angle to the horizon.
In conclusion, we note that the concept of speed, of course, is not only found in mechanics, and therefore, students studying other areas of physics (electrostatics, magnetostatics, molecular physics) also encounter the movement of particles (including charged ones), where they learn to find the speed the movement of molecules and atoms.