# Uniform linear motion

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 Pitself from the origin of the reference system.

The speed

Consider the two x positions1and x2of the same point P in two successive instants of time t1and t2; this means that, in the time interval t2- t1it is defined as average speed ( seem) of P a quantity that expresses the relationship between the space traveled x2- x1and the time taken to travel it t2- t1:

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 x2- x1or t2- t1they 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 t1, t2, t3, t4etc. 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 s0different 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 , s0).

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.