The **constant velocity motion**, also known as **uniform rectilinear motion (u.r.m.)**, is the one with ** constant velocity**, i.e., the trajectory is a straight line and the speed is constant. In this section we are going to explain:

## Definition of constant velocity motion

While finding **rectilinear uniform motion** or **constant velocity motion** in nature is quite rare, it is the easiest to study motion and it will be useful in studying other more complex motions. The **uniform rectilinear motion** has the following properties:

- The
*acceleration is zero*(*a=0*) because neither the magnitude nor the direction change - On the other hand, the
*initial, average and instantaneous velocities*have the same values at all times

A body has **constant velocity motion** or **uniform rectilinear motion** when its * trajectory is a straight line* and its

*. This implies that*

**velocity is constant***it covers equal distances in equal times*.

## Equations of constant velocity motion

Rectilinear and Uniform Motion

Equal times are spent in traveling equal distances. The average speed is constant and equal to the velocity magnitude.

The **equations of constant velocity motion** are:

Where:

*x*,*x*:_{0}of the body at a given time (*Position**x*) and at the initial time (*x*). Its unit in the International System (S.I.) is the meter (m)_{0}*v*,*v*:_{0}of the body at a given time (*Velocity**v*) and at the initial time (*v*). Its unit in the International System (S.I.) is meter per second (m/s)_{0}*a*:of the body. Its unit of measure in the International System (S.I.) is the meter per second squared (m/s**Acceleration**^{2})

To deduce the **equations of uniform rectilinear motion u.r.m.** it should be should be taken into consideration that:

- Average velocity coincides with instantaneous velocity
- There is no acceleration

With these restrictions, we get:

$$\left.\begin{array}{c}{v}_{avg}=v\\ {v}_{avg}=\frac{\mathrm{\Delta}x}{\mathrm{\Delta}t}=\frac{x-{x}_{0}}{t-{t}_{0}}\underset{{t}_{0}=0}{\underset{\u23df}{=}}\frac{x-{x}_{0}}{t}\end{array}\right\}\to x-{x}_{0}=v\cdot t\to \overline{)x={x}_{0}+v\cdot t}$$