The everyday concept of velocity arises when we consider how *quick* or *slow* a body is moving. Somehow we relate the *displacement* of the body with the *time* invested in it. In this section, we will define what is meant in physics by **average velocity**. This concept will help us understand other definitions related to velocity, that we will see in subsequent sections

## Average velocity

The **average velocity** of a body that moves *between two points P _{1} and P_{2}* is defined as the

*between the*

**ratio****and the**

*displacement vector**in which the displacement takes place. Its expression is given by:*

**time interval**where:

: Average velocity vector in the time studied${\overrightarrow{v}}_{avg}$ : Displacement vector in the time studied$\u2206\overrightarrow{r}$ : Time taken by the body to complete the displacement$\u2206t$ ,$\overrightarrow{{r}_{1}}$ : Position vectors of the corresponding initial$\overrightarrow{{r}_{2}}$ *P*and final_{1}*P*positions_{2}*t*,_{1}*t*: Time in which the body is in the initial_{2}*P*and final_{1}*P*points respectively_{2}

Additionally, the average velocity vector meets the following:

- If we use units of the International System (S.I.) in both the numerator (meters) and the denominator (seconds), we can deduce the
**dimensional equation of the average velocity****[v]=[L][T]**^{-1} - The
for velocity is*unit of measurement in the International System (S.I.)***meter per second (m/s)** - The magnitude (the "size" of the vector) is equal to the magnitude of the displacement vector divided by the elapsed time
- The direction is the same as the direction of the displacement vector

Average velocity

The average velocity of a body (green) is a vector that has the same direction as the displacement vector (blue) and its magnitude is the ratio between the magnitude of the displacement vector and the elapsed time.

It is important to notice that the average velocity of a body in a time interval depends of the position vectors at the beginning and at the end of the motion. Although it may seem paradoxical, this implies that *if the initial and final position coincide in that interval, the average velocity of the body will be 0*.