To find the correct average velocity from the given options, we'll use the formula:

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

Step 1: Calculate the total displacement.

The train travels a total distance of:

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

Step 2: Determine the total time.

The total time includes the time taken to travel 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, calculate the average velocity:

$\text{Average Velocity} = \frac{20 \text{ km}}{145 \text{ s}} \approx 0.1379 \text{ km/s}$

Step 4: Choose the closest option.

The calculated average velocity of approximately 0.1379 km/s is closest to 0.14 km/s.

Thus, the correct answer is 0.14 km/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 train traveled an additional 5 km in the same time?
2. What is the significance of stopping time when calculating average velocity?
3. How does average speed differ from instantaneous speed?
4. How would the average velocity differ if the train had different speeds in each segment?
5. Can the average velocity ever be higher than the highest speed reached during the journey?

Tip: When comparing calculated values to options, always round to the same precision as the options provided.