## Statement

If a body is in the position (1,2) and after 2 seconds it is in the position (1,-2).

What will be its average velocity considering that all units are expressed in the International System?

## Solution

Since we are using International System units, the two positions respectively called P_{i} and P_{f} are expressed in meters.

**Initial data**

P_{i} (1,2) m y P_{f}(1,-2) m.

Δt=t_{2}-t_{1}=2 sg.

**Resolution**

To calculate the average velocity, we must use of the following equation:

where the time elapsed is already provided in the statement and the displacement vector is obtained of the following way:

Therefore, first we calculate the displacement vector regarding these two positions:

$$\overrightarrow{\Delta r}=(1-1)\xb7\overrightarrow{i}+(-2-2)\xb7\overrightarrow{j}m\Rightarrow \phantom{\rule{0ex}{0ex}}\overrightarrow{\Delta r}=\left(0\right)\xb7\overrightarrow{i}+(-4)\xb7\overrightarrow{j}m\Rightarrow \phantom{\rule{0ex}{0ex}}\overline{)\overrightarrow{\Delta r}=-4\xb7\overrightarrow{j}m}$$

Once we know the displacement vector, we can calculate the average velocity vector.

$${\overrightarrow{v}}_{avg}=\frac{-4\xb7\overrightarrow{j}}{2}m\Rightarrow \phantom{\rule{0ex}{0ex}}\overline{){\overrightarrow{v}}_{avg}=-2\xb7\overrightarrow{j}m}$$