To find the average velocity of the railroad train over the entire distance, we need to follow a few clear steps. Let’s break the problem down:
1. Calculate the time taken for each segment of the trip:
- For the first segment:
- Distance: 1,000 meters
- Velocity: 80.0 m/s
- Time for the first segment: [tex]\( \text{time}_1 = \frac{\text{distance}_1}{\text{velocity}_1} = \frac{1000 \text{ m}}{80.0 \text{ m/s}} = 12.5 \text{ s} \)[/tex]
- For the second segment:
- Distance: 1,000 meters
- Velocity: 50.0 m/s
- Time for the second segment: [tex]\( \text{time}_2 = \frac{\text{distance}_2}{\text{velocity}_2} = \frac{1000 \text{ m}}{50.0 \text{ m/s}} = 20.0 \text{ s} \)[/tex]
2. Determine the total distance and total time:
- Total distance: [tex]\( \text{distance}_\text{total} = \text{distance}_1 + \text{distance}_2 = 1000 \text{ m} + 1000 \text{ m} = 2000 \text{ m} \)[/tex]
- Total time: [tex]\( \text{time}_\text{total} = \text{time}_1 + \text{time}_2 = 12.5 \text{ s} + 20.0 \text{ s} = 32.5 \text{ s} \)[/tex]
3. Calculate the average velocity:
- The average velocity is defined as the total distance divided by the total time:
- [tex]\( \text{average velocity} = \frac{\text{total distance}}{\text{total time}} = \frac{2000 \text{ m}}{32.5 \text{ s}} = 61.53846153846154 \text{ m/s} \)[/tex]
Given the choices provided:
- 63.7 m/s
- 61.5 m/s
- 65.0 m/s
- 70.0 m/s
The closest value to our calculated average velocity is 61.5 m/s.
Thus, the average velocity of the railroad train is 61.5 m/s.
