A body travels a distance `s_(1)` with vleocity `v_(1)` and distance `s_(2)` with velocity `v_(2)` in the with velocity `v_(2)` . Calculate the average velocity.

Answer

To calculate the average velocity of a body that travels two different distances with different velocities, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Quantities:**
- Distance traveled in the first segment: \( s_1 \)
- Velocity during the first segment: \( v_1 \)
- Distance traveled in the second segment: \( s_2 \)
- Velocity during the second segment: \( v_2 \)

2. **Calculate the Time Taken for Each Segment:**
- The time taken to travel the first distance \( s_1 \) with velocity \( v_1 \) is given by:
\[ t_1 = \frac{s_1}{v_1} \]
- The time taken to travel the second distance \( s_2 \) with velocity \( v_2 \) is given by:
\[ t_2 = \frac{s_2}{v_2} \]

3. **Calculate the Total Distance:**
- The total distance traveled by the body is the sum of the two distances:
\[ \text{Total Distance} = s_1 + s_2 \]

4. **Calculate the Total Time:**
- The total time taken for the entire journey is the sum of the two times:
\[ \text{Total Time} = t_1 + t_2 = \frac{s_1}{v_1} + \frac{s_2}{v_2} \]

5. **Calculate the Average Velocity:**
- The average velocity \( v_{\text{avg}} \) is defined as the total distance divided by the total time:
\[ v_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{s_1 + s_2}{\frac{s_1}{v_1} + \frac{s_2}{v_2}} \]

### Final Formula:
Thus, the average velocity can be expressed as:
\[ v_{\text{avg}} = \frac{s_1 + s_2}{\frac{s_1}{v_1} + \frac{s_2}{v_2}} \]