Converting Between Kilometers per Hour and Meters per Second

Quick Conversion Methods

• Kilometers per hour (km/h) to meters per second (m/s):
  • Divide the value by 3.6
• Meters per second (m/s) to kilometers per hour (km/h):
  • Multiply the value by 3.6

Detailed Conversion Process

Converting from Kilometers per Hour to Meters per Second

1. Example: Convert 40 km/h to m/s

   • Start with the given value: 40 km/h
   • Conversion factors:
     • 1 kilometer = 1000 meters
     • 1 hour = 60 minutes
     • 1 minute = 60 seconds
   • Steps:
     • Convert kilometers to meters:
       • Use the fraction with 1 km at the bottom and 1000 meters at the top
     • Convert hours to seconds:
       • Convert hours to minutes: 1 hour on top, 60 minutes on the bottom
       • Convert minutes to seconds: 1 minute on the bottom, 60 seconds on top
   • Calculation:
     • Multiply the numbers on the top and divide by the numbers on the bottom:
       • 40 * 1000 / 60 / 60 = 11.1 m/s

2. Practice Example: Convert 75 km/h to m/s

   • Quick method: 75 / 3.6 = 20.83 (repeating) m/s
   • Show work using detailed steps as above
   • Final result: 20.83 m/s*

Converting from Meters per Second to Kilometers per Hour

1. Example: Convert 24 m/s to km/h

   • Quick method: 24 * 3.6 = 86.4 km/h
   • Show work:
     • Start with 24 m/s
     • Conversion factors:
       • 1 kilometer = 1000 meters
       • 60 seconds = 1 minute
       • 60 minutes = 1 hour
     • Steps:
       • Convert meters to kilometers:
         • Use the fraction with 1000 meters at the bottom and 1 km on top
       • Convert seconds to minutes:
         • Use the fraction with 60 seconds on the top and 1 minute on the bottom
       • Convert minutes to hours:
         • Use the fraction with 60 minutes on top and 1 hour on the bottom
   • Calculation:
     • 24 / 1000 * 60 * 60 = 86.4 km/h

2. Practice Example: Convert 19 m/s to km/h

   • Quick method: 19 * 3.6 = 68.4 km/h
   • Show work using detailed steps as above
   • Final result: 68.4 km/h

Summary

• To convert between km/h and m/s, use 3.6 as the conversion factor (divide for km/h to m/s and multiply for m/s to km/h).
• The detailed method involves converting units step by step using fractions to cancel out units.

Tips

• Always set up your conversion with the units you want to cancel opposite each other.
• Check that all units except the desired ones are canceled out in your final result.