To convert the speed of a car driving at 46.41 miles per hour to meters per second, follow these steps:
1. Convert miles per hour to feet per hour:
- There are 5280 feet in one mile.
- Therefore, the speed in feet per hour is calculated as follows:
[tex]\[
\text{Speed in feet per hour} = 46.41 \, \text{miles per hour} \times 5280 \, \text{feet per mile} = 245044.8 \, \text{feet per hour}
\][/tex]
2. Convert feet per hour to inches per hour:
- There are 12 inches in one foot.
- Therefore, the speed in inches per hour is calculated as follows:
[tex]\[
\text{Speed in inches per hour} = 245044.8 \, \text{feet per hour} \times 12 \, \text{inches per foot} = 2940537.6 \, \text{inches per hour}
\][/tex]
3. Convert inches per hour to centimeters per hour:
- There are 2.54 centimeters in one inch.
- Therefore, the speed in centimeters per hour is calculated as follows:
[tex]\[
\text{Speed in centimeters per hour} = 2940537.6 \, \text{inches per hour} \times 2.54 \, \text{cm per inch} = 7468965.503999999 \, \text{cm per hour}
\][/tex]
4. Convert centimeters per hour to meters per second:
- There are 100 centimeters in one meter and 3600 seconds in one hour.
- Thus, the speed in meters per second is calculated as follows:
[tex]\[
\text{Speed in meters per second} = \frac{7468965.503999999 \, \text{cm per hour}}{100 \, \text{cm per meter} \times 3600 \, \text{seconds per hour}} = 20.7471264 \, \text{meters per second}
\][/tex]
After following these conversion steps, we find that the car is driving at approximately [tex]\(20.75\)[/tex] meters per second.
