The speed limit on some interstate highways is roughly 125 km/h.
A. What is this in meters per second?
B. How many miles per hour is this?
The Correct Answer and Explanation is:
A. Conversion to meters per second:
To convert a speed of 125 kilometers per hour (km/h) to meters per second (m/s), we can use the following relationship:
1 kilometer = 1,000 meters
1 hour = 3,600 seconds
Thus, the conversion factor from kilometers per hour to meters per second is:
[
\text{1 km/h} = \frac{1,000 \, \text{meters}}{3,600 \, \text{seconds}} = \frac{5}{18} \, \text{m/s}
]
Now, to convert 125 km/h to m/s:
[
125 \, \text{km/h} = 125 \times \frac{5}{18} \, \text{m/s}
]
[
125 \times \frac{5}{18} = \frac{625}{18} \approx 34.72 \, \text{m/s}
]
Thus, 125 km/h is approximately 34.72 meters per second.
B. Conversion to miles per hour:
To convert 125 kilometers per hour (km/h) to miles per hour (mph), we need to know that:
1 kilometer ≈ 0.621371 miles
So, the conversion factor from kilometers to miles is 0.621371. To convert 125 km/h to miles per hour:
[
125 \, \text{km/h} \times 0.621371 \, \text{miles/km} = 77.671375 \, \text{miles per hour}
]
Thus, 125 km/h is approximately 77.67 miles per hour.
Explanation:
The conversion from kilometers per hour to meters per second involves converting the larger unit of kilometers to meters, which gives a factor of 1,000. At the same time, the conversion from hours to seconds is done by dividing by 3,600 (the number of seconds in an hour). The final multiplication by (\frac{5}{18}) gives the result in meters per second.
For converting kilometers per hour to miles per hour, the key step is recognizing that 1 kilometer is approximately 0.621371 miles. This factor is used to convert the speed to miles per hour, providing a meaningful comparison in terms of miles, the standard unit used in many countries like the United States.