A train travels 10 km for 50 seconds and then stops for 20 seconds. It then travels another 10 km for 75 seconds. What is the train's average velocity during all 145 seconds?



To find the train's average velocity over the entire 145 seconds, we need to calculate the total distance traveled and divide it by the total time taken.

### Step 1: Calculate the total distance traveled
- The train travels 10 km in the first segment.
- The train travels another 10 km in the second segment.

Total distance traveled = \(10 \, \text{km} + 10 \, \text{km} = 20 \, \text{km}\)

### Step 2: Calculate the total time taken
- Time spent traveling in the first segment = 50 seconds
- Time spent stopping = 20 seconds
- Time spent traveling in the second segment = 75 seconds

Total time taken = \(50 \, \text{seconds} + 20 \, \text{seconds} + 75 \, \text{seconds} = 145 \, \text{seconds}\)

### Step 3: Calculate the average velocity
Average velocity \(v_{avg}\) is given by:

\[
v_{avg} = \frac{\text{Total distance}}{\text{Total time}}
\]

Convert the total distance from kilometers to meters:

\[
\text{Total distance} = 20 \, \text{km} = 20,000 \, \text{m}
\]

Now, calculate the average velocity:

\[
v_{avg} = \frac{20,000 \, \text{m}}{145 \, \text{seconds}} \approx 137.93 \, \text{m/s}
\]

### Answer:
The train's average velocity during all 145 seconds is approximately **137.93 m/s**.

Would you like more details on any part of the solution? Here are some related questions:

1. How do you convert km/h to m/s and vice versa?
2. What is the difference between speed and velocity?
3. How do you calculate the average speed if the train had multiple stops?
4. What would be the average velocity if the stopping time was different?
5. How does uniform acceleration affect the average velocity?

**Tip:** Average velocity considers both the magnitude and the direction of the displacement, making it a vector quantity, unlike average speed, which is scalar.

Learn how to calculate the average velocity of a train based on distance and time traveled, including stopping periods. This problem involves kinematics and the application of average velocity formulas. Suitable for students in Grades 9-12.

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