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To understand average velocity, consider it as the total displacement divided by the total time taken. It takes into account all the movements and pauses experienced in the time interval.
In our exercise, the man initially stands still for 5 minutes, then moves at a constant speed for the next 5 minutes. This means his motion involves a phase of no movement and a phase of consistent motion.

For the time interval between 2 minutes (120 seconds) and 8 minutes (480 seconds), he begins moving at the 5-minute mark (300 seconds). Only this movement is considered for calculating average velocity.
The formula used is:
\[v_{\text{avg}} = \frac{\text{Total Distance Traveled}}{\text{Total Time}}\]
- For the interval from 2 min to 8 min, he covers 396 meters in 360 seconds, giving an average velocity of 1.10 m/s.
- For the interval from 3 min to 9 min, he covers 528 meters also in 360 seconds, resulting in a higher average velocity of 1.47 m/s.

This analysis shows how changes in movement affect average velocity over different periods.

Average acceleration is the change in velocity over a period of time. It tells us how quickly an object's velocity changes. In our scenario, the man transitions from standing still to walking at 2.20 m/s.
The average acceleration can be calculated keeping in mind the time intervals in which the change occurred. Since velocity increases from 0 to 2.20 m/s only when he starts walking, only the duration of his walk impacts the calculation.

The formula for average acceleration is:
\[a_{\text{avg}} = \frac{\Delta v}{\Delta t}\]
Where \(\Delta v\) is the change in velocity and \(\Delta t\) is the time taken for this change.
- From 2 minutes to 8 minutes, \(\Delta v = 2.20 \text{ m/s} - 0\), over 360 seconds, resulting in an average acceleration of approximately 0.0061 m/s².
- Likewise, for 3 minutes to 9 minutes interval, using the same change in velocity over the same time, the average acceleration remains approximately 0.0061 m/s².

Understanding how velocity changes help to comprehend the concept of acceleration, even when motion seems uniform.

Motion graphs allow us to visualize an object's movement over time. Analyzing graphs helps connect visual data to motion concepts like velocity and acceleration.

**Position vs. Time Graph**: This graph shows how far the man has moved at each moment in time. In this case: - A horizontal line at the beginning (0 to 300 seconds) represents standing still as there is no change in position. - A diagonal, upward line from 300 seconds onward illustrates constant motion with a steady increase in position. The slope represents average velocity.
**Velocity vs. Time Graph**: This graph reflects how the man's speed changes over time. - A flat line at zero for the first 300 seconds signifies no movement. - A flat line at 2.20 m/s from 300 seconds onwards shows constant velocity movement. With no change in line height here, the average acceleration is represented by small changes in speed when it first occurs.

By analyzing these graphs, you can easily see where changes in motion, such as standing still or moving, occur and how they relate to calculated values of average velocity and acceleration.