Explanation:
To understand the numerical ratio of average velocity to average speed, let's first define these terms:

Average Velocity: Average velocity is the displacement divided by the time taken. It is a vector quantity and includes both magnitude and direction. The formula for average velocity is:

Average velocity = Displacement / Time taken

Average Speed: Average speed is the total distance traveled divided by the time taken. It is a scalar quantity and only includes magnitude. The formula for average speed is:

Average speed = Total distance / Time taken

Now, let's consider the numerical ratio of average velocity to average speed:

Ratio of average velocity to average speed:
The ratio of average velocity to average speed can be calculated by dividing the average velocity by the average speed:

Ratio = Average velocity / Average speed

Since average velocity is the displacement divided by time taken, and average speed is the total distance divided by time taken, the ratio can be simplified as:

Ratio = (Displacement / Time taken) / (Total distance / Time taken)

The time taken cancels out, giving us:

Ratio = Displacement / Total distance

Understanding the ratio:
The ratio of displacement to total distance is always equal to or less than one. This is because the magnitude of displacement (which determines the average velocity) can never be greater than the magnitude of total distance (which determines the average speed). Displacement is the shortest path between two points, whereas total distance is the actual path traveled.

Conclusion:
Therefore, the numerical ratio of average velocity to average speed is always equal to or less than one. This means that the average velocity is always equal to or less than the average speed.

Equal to or less than one because displacement is always less than or equal to distance