Calculation of average velocity

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=t₂-t₁=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:

$$\begin{gathered} \overrightarrow{\Delta r}=(1-1)·\overrightarrow{i}+(-2-2)·\overrightarrow{j}m \Rightarrow \\ \overrightarrow{\Delta r}=\left(0\right)·\overrightarrow{i}+(-4)·\overrightarrow{j} m\Rightarrow \\ \boxed{\overrightarrow{\Delta r}=-4 ·\overrightarrow{j}m} \end{gathered}$$

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

$$\begin{gathered} {\overrightarrow{v}}_{avg}=\frac{-4·\overrightarrow{j}}{2}m \Rightarrow \\ \boxed{{\overrightarrow{v}}_{avg}=-2 ·\overrightarrow{j }m} \end{gathered}$$