To find the train's average velocity over the entire 145 seconds, we'll use the formula for average velocity:

$\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}}$

Step 1: Calculate the total displacement.

The train travels 10 km in the first segment and 10 km in the second segment, so the total displacement is:

$\text{Total Displacement} = 10 \text{ km} + 10 \text{ km} = 20 \text{ km}$

Step 2: Determine the total time.

The total time includes the time taken to travel each segment and the time spent stopped:

$\text{Total Time} = 50 \text{ s} + 20 \text{ s} + 75 \text{ s} = 145 \text{ s}$

Step 3: Calculate the average velocity.

Now, plug the values into the formula for average velocity:

$\text{Average Velocity} = \frac{20 \text{ km}}{145 \text{ s}}$

Step 4: Convert the units if necessary.

Since velocity is typically expressed in meters per second (m/s), we'll convert the displacement from kilometers to meters:

$20 \text{ km} = 20,000 \text{ m}$

Now, the average velocity is:

$\text{Average Velocity} = \frac{20,000 \text{ m}}{145 \text{ s}} \approx 137.93 \text{ m/s}$

So, the train's average velocity over the 145 seconds is approximately 137.93 m/s.

Would you like more details or have any questions?

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Here are 5 related questions for further exploration:

1. How would the average velocity change if the stop time was reduced to 10 seconds?
2. What would be the train's average speed if it traveled 15 km in the first segment and 5 km in the second segment?
3. How does the concept of average speed differ from average velocity?
4. If the train had accelerated or decelerated during each segment, how would you calculate the average velocity?
5. What is the significance of uniform motion in calculating average velocity?

Tip: When calculating average velocity, always ensure that the total displacement and total time are considered, rather than focusing on individual segments.