To calculate the train's average velocity during the entire 145 seconds, we need to determine the total distance traveled and the total time taken.

Step 1: Calculate the total distance traveled

The train travels two segments:

1. First segment: $10$ km
2. Second segment: $10$ km

So, the total distance traveled by the train is: $\text{Total distance} = 10 \, \text{km} + 10 \, \text{km} = 20 \, \text{km}$

Step 2: Calculate the total time taken

The total time includes both the time the train is moving and the time it is stopped:

1. Time moving in the first segment: $50$ seconds
2. Stopping time: $20$ seconds
3. Time moving in the second segment: $75$ seconds

Thus, the total time is: $\text{Total time} = 50 \, \text{seconds} + 20 \, \text{seconds} + 75 \, \text{seconds} = 145 \, \text{seconds}$

Step 3: Calculate the average velocity

Average velocity is given by the total distance traveled divided by the total time taken: $\text{Average velocity} = \frac{\text{Total distance}}{\text{Total time}} = \frac{20 \, \text{km}}{145 \, \text{seconds}}$

Step 4: Convert to kilometers per hour (optional)

To express the average velocity in km/h: $\text{Average velocity} = \frac{20 \, \text{km}}{145 \, \text{seconds}} \times \frac{3600 \, \text{seconds}}{1 \, \text{hour}}$ $\text{Average velocity} = \frac{20 \times 3600}{145} \, \text{km/h} \approx 496.55 \, \text{km/h}$

So, the average velocity of the train during the 145 seconds is approximately 496.55 km/h.

Would you like more details or have any questions?

Related Questions:

1. How would the average velocity change if the stopping time was doubled?
2. What would the average speed be if the train only traveled the first segment?
3. How does the average velocity differ from average speed in this scenario?
4. What is the significance of the train stopping in terms of velocity calculation?
5. How would you calculate the average velocity if the train traveled different distances at different speeds?

Tip: Remember, average velocity depends on the total displacement and total time, not just the time when the object is moving.