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To convert \( 32 \, \text{m/s} \) to miles per hour (mph) using the given conversion \( 8 \, \text{km/h} = 5 \, \text{mph} \), we'll follow these steps:

1. **Convert \( 32 \, \text{m/s} \) to km/h**:
   - We know that \( 1 \, \text{m/s} = 3.6 \, \text{km/h} \).
   - So, \( 32 \, \text{m/s} \times 3.6 = 115.2 \, \text{km/h} \).

2. **Use the conversion factor** \( 8 \, \text{km/h} = 5 \, \text{mph} \):
   - To convert \( 115.2 \, \text{km/h} \) to mph, use the ratio of the conversion:
   \[
   \frac{5 \, \text{mph}}{8 \, \text{km/h}} \times 115.2 \, \text{km/h} = \frac{5}{8} \times 115.2 = 72 \, \text{mph}
   \]

So, \( 32 \, \text{m/s} = 72 \, \text{mph} \).

Would you like more details on any part of this process? Here are some follow-up questions to explore further:

1. How do you derive the relationship between meters per second and kilometers per hour?
2. What are other common conversions between metric and imperial speed units?
3. How can you calculate the conversion factor for different speeds?
4. What are some real-life scenarios where this type of conversion is important?
5. How would the conversion change if the initial velocity was given in a different unit?

**Tip**: Always remember that multiplying by \( 3.6 \) is the easiest way to convert from meters per second to kilometers per hour.

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

Learn how to convert 32 m/s into mph using the conversion factor 8 km/h = 5 mph. This problem demonstrates the conversion from meters per second to miles per hour, with the key concept of using ratios for unit conversions. Suitable for high school students.

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