The simplest type of movement of a body is constituted by rectilinear motion, where its trajectory is reduced to a straight line and the hourly law can be expressed through the variation over time of only one of the three coordinates (usually the *x* ). At each instant, the position of the point *P* can thus be represented by a displacement vector having:

- direction coinciding with the straight path of motion;
- verse in the direction of the movement of
*P*; - intensity, or modulus, equal to the distance of
*P*itself from the origin of the reference system.

**The speed**

Consider the two *x* positions1and *x*2of the same point *P* in two successive instants of time *t*1and *t*2; this means that, in the time interval *t*2- *t*1it is defined as average speed ( *see*m) of *P* a quantity that expresses the relationship between the space traveled *x*2- *x*1and the time taken to travel it *t*2- *t*1:

In physics, the variation of a quantity (such as space *x* or time *t* ) is preferably indicated by the capital Greek letter Δ (delta), which represents an increase; the differences *x*2- *x*1or *t*2- *t*1they can therefore be expressed by the notations Δ *x* and Δ *t* ; the definition of average speed then takes the form:

where the ratio Δ *x /* Δ *t* is called the incremental ratio.

If we consider various successive instants *t*1, *t*2, *t*3, *t*4etc. for each time interval considered, this ratio is constant: the point *P* is said to move with uniform rectilinear motion, i.e. it travels equal spaces in equal time intervals, with speed given by the vector **v** , having direction along the trajectory, towards in the sense of motion and intensity:

More generally, in the case of a uniform rectilinear motion it is possible to express the speed as a constant ratio between the space traveled *s* and the time used *t* through the simple relationship:

from which the hourly law of uniform rectilinear motion is obtained:

In the event that, at the initial instant *t* = 0, the moving body is in an initial position *s*0different from the origin ( *O* ) of the reference system, the hourly law of uniform rectilinear motion takes the more general form:

This hourly law, represented graphically in a Cartesian plane having the time *t* in the abscissa and the space *s* in the ordinate , corresponds to a straight line (see fig. 3.2), which intersects the axis ( *s* ) of the ordinates at the coordinate point ( *Or* , *s*0).

Speed has the dimensions of a space divided once. In the International System, the unit of measurement for speed is that of a body that travels 1 meter (m) of space in 1 second (s) of time; this unit is indicated with the symbol m / s, which reads “meter per second”. A second commonly used unit of measurement for speed is the kilometer per hour (km / h), where 1 km / h = 0.278 m / s. Consequently 1m / s = 3.6 km / h.