Conversion of Units

The solution to many problems in science requires changing units of measurements from one system to another.

The following method is simple and easy once it is understood. An understanding of this method can be gained by solving several practice problems.

What is the distance in feet traveled  by an automobile in 10 s, if the average speed of the car is 60 mi/h? Because we want to know the distance traveled in feet, we must convert miles per hour to feet per second. This can be done as follows:

1. Write down the term you want to convert and set it equal to itself. At the same time, make a mental or written note of the terms to      which you wish to convert.

2. Multiply the right side of the equation by 1 or by 1/1, which is the same thing. It does not change its actual value.

3. Place a unit in the numerator or denominator of the 1/1 that will cancel out an unwanted unit in the original term. In this case, we would place the unit "mile" in the denominator. At the same time, place an equal term above our newly introduced denominator unit, in order to keep the value equal to 1/1. Because we are after feet in our answer for this problem, use 5280 ft in the numerator of the 1/1, because that is equal to 1 mi. Then cancel like units.

4. The next step is to eliminate the unit hour in the denominator. This can be accomplished by multiplying again by 1/1 and placing the unit hour in the numerator of the 1/1 term. At the same time, an equal unit should be placed in the denominator of the 1/1 term in order to keep the value equal to 1/1. Because 60 min equal 1 h, we can use it and then cancel both "hour" terms.

5. At this point, we have feet per minute, but we want feet per second; therefore we must convert the minutes to seconds. Again we multiply by 1 of 1/1 and add the appropriate units for conversion.

6. After all like units are cancelled, the numbers are cancelled insofar as is possible; we arrive at

or after dividing,

The problem can now be solved using 88 ft/s for 60 mi/h. Knowing that

d = vt

and substituting

we obtain

d = 880 ft