Movement body occurs along some trajectory.In the case of linear motion it is a straight line, so to find the movement body quite simple: it is equal to the distance traveled.Otherwise, it can determine the coordinates for the start and end positions in space.
amount of movement of a material point is a vector because it has a direction.Therefore, to find its numerical value, you need to calculate the unit vector connecting the start point and the way it ends.
Consider the two-dimensional coordinate space.Let the body made the journey from point A (x0, y0) to point B (x, y).Then, to find the length of the vector AB, lower projections of its ends on the abscissa and ordinate.Geometrically relative to the projection and the other coordinate axis can be represe
nted as the legs of a right triangle with lengths: Sx = x - x0; Sy = y - y0, where Sx and Sy - the projection of the vector on the respective axes.
unit vector, ie,the length of the body movement , in turn, is the hypotenuse of the triangle, which is easy to determine the length of the Pythagorean theorem.It is equal to the square root of the sum of the squares of the projections: S = √ (Sx² + Sy²).
in three-dimensional space: S = √ (Sx² + Sy² + Sz²), where Sz = z - z0.
This formula is common to any kind of movement.The displacement vector has a number of features: • its magnitude can not exceed the length of the distance traveled; • projection of moving can be both positive and negative, while the value of the path is always greater than zero; • generally moving does not coincide with the trajectory body movement , and his unit is not the way.
In the particular case of rectilinear motion of the body is moved along only one axis, for example, the x-axis.Then the length is equal to the difference between the movement and the start of the first end point coordinates: S = x - x0.