A review of the problems on the question of how to find speed in the school courses of mathematics and physics

The concept of speed is one of the key in the characteristic of the dynamic parameters of a single object, as well as of some system. Indeed, speed is the most important physical quantity that characterizes movement, and with the concept of motion, a person encounters in his life constantly. And it does not matter, we mean the movement of molecules or multi-ton trucks, a pedestrian or a multi-meter train. 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 this attention is attached to this parameter not only with the fact that the person is constantly confronted with the movement, but also because the concept of speed has a diverse character.

The first tasks on how to find speed are met by the pupils in the mathematics course of primary school (as a rule, these are grades 3 and 4). Of course, these problems are elementary and are devoted to the consideration of the ideal model of mechanical motion. Familiarization with the mathematical description of the displacement of bodies begins with the most important concepts - the path, speed and time - and the well-known formula that the path is the product of the speed of motion at the time of displacement.

At the same stage in the mathematics school course, the concept of productivity is considered, telling students how to find the speed of production. This approach is very advisable, because the mathematical descriptions of these processes are similar, and, consequently, it will be easier for students to understand the meaning of at first sight very complex definitions of work and productivity.

After mastering the elementary laws of mechanical motion, with the example of one body, students become acquainted with the phenomenon of motion of several bodies simultaneously. Of course, in elementary school, this process is considered in elementary examples and ideal models. Students solve problems and learn how to find the speed of rapprochement if one body catches up with another or two bodies move towards each other.

The tasks devoted to speed continue to meet the students in the middle section of the school course of mathematics. In the fifth grade, students get acquainted with the concept of average speed. It is very important to emphasize that the average speed and the arithmetic mean are different values. Often pupils confuse these concepts, projecting the formula for calculating the arithmetic mean for tasks devoted to movement. It is important to explain how to find the speed if the motion is made at different, different from each other time intervals with different speeds.

More complex phenomena of mechanical motion are considered in the school course of physics, which begins to be studied by students in the 7th grade. First, elementary concepts of motion related to questions are also considered here, how to find the initial velocity of the body's motion before the moment of acceleration, or how to calculate the path traveled by the body to a certain point in time.

In the 9th form, students get acquainted with the concept of displacement and its difference from the path. At the same stage of studying the mechanical movement, students are introduced to solutions of classical problems on how to find the speed of convergence of bodies moving at an angle to each other and, in particular, perpendicularly.

The course of mechanics continues also in the senior link of the school course of physics, but here the emphasis is on solving problems related to the motion of a multitude of bodies or with complex displacements of one body. For example, in the 10th grade, much time is devoted to tasks dedicated to the movement of the body at an angle to the horizon.

In conclusion, we note that the concept of speed, of course, occurs not only in mechanics, and therefore students in studying other branches of physics (electrostatics, magnetostatics, molecular physics) also face the motion of particles (including charged ones), where they learn to find the speed Displacement of molecules and atoms.