25m/s to miles/hr step by step
The Correct Answer and Explanation is :
Conversion: 25 m/s to miles per hour
To convert 25 meters per second (m/s) to miles per hour (mph), follow these steps:
Step 1: Understand the relationship between units
- (1 \, \text{meter} = 0.001 \, \text{kilometers})
- (1 \, \text{kilometer} = 0.621371 \, \text{miles})
- (1 \, \text{second} = \frac{1}{3600} \, \text{hours})
Step 2: Convert meters per second to kilometers per second
[
25 \, \text{m/s} \times 0.001 \, \text{km/m} = 0.025 \, \text{km/s}
]
Step 3: Convert kilometers per second to kilometers per hour
Since there are 3600 seconds in an hour:
[
0.025 \, \text{km/s} \times 3600 \, \text{s/hour} = 90 \, \text{km/h}
]
Step 4: Convert kilometers per hour to miles per hour
Using the conversion factor (1 \, \text{km} = 0.621371 \, \text{miles}):
[
90 \, \text{km/h} \times 0.621371 \, \text{miles/km} = 55.92339 \, \text{mph}
]
Final Answer:
[
25 \, \text{m/s} = 55.92 \, \text{mph} \, (\text{rounded to 2 decimal places})
]
Explanation (300 Words):
To convert 25 m/s to mph, we go through two unit changes: distance and time. First, meters are converted to kilometers, and then kilometers to miles because miles are not a direct metric unit. Simultaneously, seconds are converted to hours to match the typical speed format.
The key to this conversion lies in understanding relationships:
- Distance: A kilometer is 1000 meters, and a mile equals about 1.609 kilometers. Therefore, to shift from metric to imperial, we multiply by (0.621371).
- Time: Speed in m/s is faster than km/h because 1 hour has 3600 seconds, requiring a multiplication factor of 3600 when converting time from seconds to hours.
The systematic approach ensures each unit transforms correctly, maintaining dimensional accuracy. After converting meters to miles and seconds to hours, the numerical magnitude grows because we’re scaling up seconds to hours but scaling down meters to miles (due to larger mile units).
This kind of conversion is crucial in fields like transportation and physics, where speed needs to be compared across systems (e.g., metric and imperial). It allows uniform communication of data regardless of local preferences in unit systems. The final result, (55.92 \, \text{mph}), accurately reflects the speed in a familiar unit for contexts like road travel.