Convert 60 miles per hour into meters per second. Solution 2. Convert 186,282 miles per second into meters per second. Solution
The Correct Answer and Explanation is:
1. Convert 60 miles per hour into meters per second
Solution:
We begin by using the conversion factors:
- 1 mile=1,609.34 meters1 \text{ mile} = 1,609.34 \text{ meters}1 mile=1,609.34 meters
- 1 hour=3,600 seconds1 \text{ hour} = 3,600 \text{ seconds}1 hour=3,600 seconds
Now, convert step by step:60 miles/hour=60×1,609.34 meters1 mile×1 hour3,600 seconds60 \text{ miles/hour} = 60 \times \frac{1,609.34 \text{ meters}}{1 \text{ mile}} \times \frac{1 \text{ hour}}{3,600 \text{ seconds}}60 miles/hour=60×1 mile1,609.34 meters×3,600 seconds1 hour=60×1,609.343,600=96,560.43,600≈26.82 m/s= \frac{60 \times 1,609.34}{3,600} = \frac{96,560.4}{3,600} \approx 26.82 \text{ m/s}=3,60060×1,609.34=3,60096,560.4≈26.82 m/s
✅ Answer: 60 miles per hour ≈ 26.82 meters per second
2. Convert 186,282 miles per second into meters per second
Solution:
This is a direct unit conversion from miles to meters:
- 1 mile=1,609.34 meters1 \text{ mile} = 1,609.34 \text{ meters}1 mile=1,609.34 meters
So,186,282 miles/second=186,282×1,609.34 meters/second186,282 \text{ miles/second} = 186,282 \times 1,609.34 \text{ meters/second}186,282 miles/second=186,282×1,609.34 meters/second=299,792,458.28 meters/second= 299,792,458.28 \text{ meters/second}=299,792,458.28 meters/second
✅ Answer: 186,282 miles per second ≈ 299,792,458 m/s
Explanation
Unit conversion is a fundamental skill in science and engineering that allows quantities to be expressed in different systems of measurement. In these problems, we are converting speeds from the Imperial system (miles per hour or miles per second) to the metric system (meters per second), which is commonly used in scientific contexts.
To perform any unit conversion, we use known equivalencies between units. For distance, 1 mile is equal to approximately 1,609.34 meters. For time, 1 hour is equal to 3,600 seconds. In Problem 1, we convert miles per hour (mph) to meters per second (m/s) by multiplying by the number of meters in a mile and dividing by the number of seconds in an hour. This two-step process ensures that both distance and time are appropriately adjusted to the target units. The result—26.82 m/s—gives us a scientific measure of a common speed, such as that of a moving vehicle.
In Problem 2, we convert the speed of light in miles per second to meters per second. This is a straightforward multiplication because the time unit (seconds) remains the same, so only the distance unit needs to be converted. The result, 299,792,458 m/s, matches the universally recognized value of the speed of light in a vacuum. This conversion underscores the importance of unit consistency in scientific measurements, where precision and accuracy are critical.
In conclusion, proper unit conversion requires careful attention to dimensional analysis, multiplication by the correct conversion factors, and clear, step-by-step calculations. This ensures that scientific values are accurately communicated across different unit systems.
