The movement of any body can be described if there is a way to determine its position in space at every moment. To do this, you need to have a body of reference, (to know what kind of object we will consider its movement), and also to establish for ourselves the way in which we will describe this movement.
Since the bodies have dimensions (that is, some extent in space), we need to decide in which cases we can neglect them and not trace the movement of each point. This is possible in two cases: if the body moves in such a way that all the straight lines drawn in it move parallel to themselves (such a motion is called translational), and also if the dimensions of the body in the conditions of the problem can be neglected (consider the body to be a material point). This happens if the path traveled by the body many times exceeds its physical dimensions.
In mechanics, by default, the body is taken as a material point, unless otherwise specified.
The line of motion of a point in space is the trajectory of motion. What it is? The concept of "trajectory", the definition of which is given by classical mechanics, implies the totality of all the positions successively occupied by a material point in space.
To determine the position that a material point occupies in space at any given moment in time, the concepts of a radius vector or coordinate system are used. The coordinates x, y, z characterize the linear location of the point relative to the corresponding axes. The formula for changing these coordinates (or the position of the radius vector) is the formula by which its trajectory of motion is determined.
Since the movement occurs not only in space, but also in time, the third component of the reference system is a device for measuring time (clock or stopwatch). Together with the coordinate system and the starting point (reference body), they form the necessary “set” for describing the motion of our material point.
Let the trajectory of movement be an arc with a beginning at point M1, whose coordinates are X1, Y1 and Z1, and ending at point M2 (coordinates X2, Y2, Z2). The distance that a material point travels along its path (the length of the arc | M1M2 |) will be called the length of its path. This value is scalar.
If we draw a directed segment (vector) r from point M1 to point M2, then it will be called the movement of the material point. This concept is not identical to the concept of the path. The path and movement of the point coincide only in the case of moving in a straight line.
The kinematic law of motion (or a method of determining its coordinates at any moment) is a function of time and can take the analytical form of a coordinate function or radius vector of the variable t, which indicates the time of movement. It can be expressed by a formula, in the form of a table or in the form of a graph.
With uniform motion, there is such a thing as the speed of a material point. Speed is the quotient of dividing the amount of displacement by travel time. If the trajectory of movement is straight, but at the same time the body moves unevenly, i.e. with different speeds in different parts of the path, then we can talk about average speed.
In mechanics, a different kind of movement is considered - uniformly rectilinear, uniformly accelerated, rectilinear and uniform in circumference.
The characteristics of mechanical motion are relative, the motion can be considered immediately in two or more coordinate systems, some of them are motionless, others are mobile. For example, a car moves along a road relative to a pedestrian walking along it (a moving point), which itself moves relative to a tree growing near the road (a fixed reference point). In this case, the speed of the body (car) will consist of two speeds - its speed relative to the first - mobile - system (pedestrian) and the speed of the pedestrian relatively stationary (tree).