The image you uploaded shows the formula for average velocity in vector form:

$\vec{v}_{\text{av}} = \frac{\vec{v}_i + \vec{v}_f}{2}$

Where:

• $\vec{v}_{\text{av}}$ represents the average velocity vector.
• $\vec{v}_i$ is the initial velocity vector.
• $\vec{v}_f$ is the final velocity vector.

This formula calculates the average velocity when acceleration is constant, and it takes the simple average of the initial and final velocities.

Would you like a detailed example of how to apply this formula or further clarifications?

Here are some follow-up questions:

1. How do you calculate average velocity if acceleration is not constant?
2. Can you derive this formula from the definition of average velocity?
3. How does this formula apply to motion in two or three dimensions?
4. What is the physical significance of the direction of velocity vectors?
5. How does this formula change in the context of non-linear motion?

Tip: When working with vectors, always remember to break them down into their components (x, y, z) if the motion occurs in multiple dimensions.