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To convert \( 32 \, \text{m/s} \) into miles per hour (mph) using the given conversion factor \( 8 \, \text{km/h} = 5 \, \text{mph} \), we need to proceed with unit conversions as follows:

### Step-by-Step Solution
1. **Convert \( 32 \, \text{m/s} \) to km/h**:
   Since \( 1 \, \text{m/s} = 3.6 \, \text{km/h} \),
   \[
   32 \, \text{m/s} \times 3.6 = 115.2 \, \text{km/h}.
   \]

2. **Use the conversion factor to get mph**:
   We know \( 8 \, \text{km/h} = 5 \, \text{mph} \). So, we can set up a proportion:
   \[
   \frac{115.2 \, \text{km/h}}{8 \, \text{km/h}} = \frac{x \, \text{mph}}{5 \, \text{mph}}.
   \]
   Solving for \( x \):
   \[
   x = \frac{115.2 \times 5}{8} = 72 \, \text{mph}.
   \]

### Answer
Thus, \( 32 \, \text{m/s} \) is equivalent to \( 72 \, \text{mph} \).

Would you like more details on any part of this solution?

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### Related Questions
1. How would you convert from mph to m/s directly without using an intermediate step?
2. If the conversion factor was \( 1 \, \text{km/h} = 0.621371 \, \text{mph} \), how would that affect the calculation?
3. How can you derive the conversion of m/s to mph from basic principles of distance and time?
4. Why is it necessary to use unit conversions in physics and engineering problems?
5. What other real-world applications require speed conversions between different units?

### Tip
When working with conversions, ensure all units are consistently applied across the equation to avoid errors.

Use the conversion 8 km/h = 5 mph to convert 32 m/s into mph.

Learn how to convert 32 meters per second (m/s) into miles per hour (mph) using the given conversion factor of 8 km/h = 5 mph. Follow the step-by-step solution to understand the conversion process.

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