Convert 31.5 miles per hour to meters per second. Report your answer to 3 significant figures.
The Correct answer and Explanation is:
To convert miles per hour (mph) to meters per second (m/s), we can use the following conversion factors:
- Miles to Meters:
- 1 mile = 1,609.34 meters.
- Hours to Seconds:
- 1 hour = 3,600 seconds.
Conversion Steps
- Start with the speed in mph:
[
31.5 \text{ miles per hour}
] - Convert miles to meters:
[
31.5 \text{ miles} \times 1,609.34 \text{ meters/mile} = 50,703.03 \text{ meters}
] - Convert hours to seconds:
[
1 \text{ hour} = 3,600 \text{ seconds}
] - Calculate meters per second:
[
\frac{50,703.03 \text{ meters}}{3,600 \text{ seconds}} \approx 14.086 \text{ m/s}
] - Round to three significant figures:
[
14.1 \text{ m/s}
]
Final Answer
Thus, ( 31.5 \text{ miles per hour} ) is approximately 14.1 m/s when reported to three significant figures.
Explanation
The conversion from miles per hour to meters per second involves understanding two key units of measurement: miles, a unit of distance primarily used in the United States, and meters, the standard unit of distance in the International System of Units (SI).
To convert the speed, we first change the distance from miles to meters using the conversion factor (1 \text{ mile} = 1,609.34 \text{ meters}). Since speed also involves time, we convert hours into seconds using the conversion factor (1 \text{ hour} = 3,600 \text{ seconds}). By dividing the total distance in meters by the total time in seconds, we obtain the speed in meters per second.
This conversion is particularly useful in scientific contexts, where SI units are preferred for consistency and clarity. Understanding these conversions is essential for applications in physics, engineering, and many everyday situations, ensuring that calculations remain accurate across different unit systems.