The correct conversion is the one in which all the units cancel out, except meters in the numerator and seconds in the denominator. Once the conversion factors are arranged so the units work out, all you have to do is multiply and divide the values as they appear in the numerator or denominator. In this example, the speed of the car is 13.4 m/s. Once the speed has been converted to units of m/s it is consistent with the distance across the intersection in meters. To solve the problem you apply the formula: t = d/v to calculate that it takes the car 1.34 seconds to cross the intersection.
In The United States, gas efficiency is measured in miles/gallon. In Europe, it is measured in km/L. If a car's gas mileage is 25 mi/gal, how many liters of gasoline would you use over a 133 km trip?
Use: 1 km = 0.62 mi and 1 gal = 3.78 L
- 9.59 L
- 13.25 L
- 12.46 L
- 10.67 L
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Answer: C
This problem has multiple conversions that must be made. In order to avoid error it is best to do them step by step. First we will convert mi/gal to km/gal:
Now we can convert km/gal to km/L:
Now with the correct units we can calculate how many liters of gasoline are needed to travel 133km:
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Speed has units of distance divided by units of time. When converting speeds, you need to use conversion factors for both time and distance. To convert the distance you might use the conversion factor 1 mile = 1609 meters. To convert the time you might use 1 hour = 3,600 seconds. The three calculations on the right show correct and incorrect ways to do the conversion. Which is correct?