Velocity

Velocity is the distance traveled in a certain direction per unit of time. When we say that we are driving 60 miles per hour, we mean that we would travel 60 miles if we maintained that speed for an hour. People often use velocity and speed interchangeably; strictly speaking, velocity also includes the direction of motion.

There are several ways of writing velocity as a ratio:

We will use the last form when we do our conversions. This form looks like a fraction, and you can perform some of the same operations on it as you would a fraction, but remember that it is a ratio.

Converting Ratios

There are 4 girls and 14 boys in our class. You could write this as:

You can also reduce this ratio to:

4 girls to 14 boys is equivalent to 2 to 7

Note that when you have two equivalent ratios, the product of the numerator on the left and the denominator on the right equals the product of the numerator on the right and the denominator on the left:

4 times 7 equals 2 times 14

Ratio Conversion Practice

  1. The ratio of boys to girls in Ms. Jones' class is 5 to 4. There are 15 boys in the class. How many girls are there?
  2. Your family is going on a trip. It is 450 miles from your home to your destination. If your average speed is 50 miles per hour, including stops, how long will it take to get there?
  3. Virginia is now offering SOL tests on the World Wide Web. In order to take Web-based tests, a school must have a ratio of 1 computer for every five students. If Marion Intermediate School has 437 students, how many computers must we have to do Web-based SOL testing? Remember that you can't have a fractional computer.
  4. Velocity Conversion

    In this assignment, you will learn to convert any velocity to miles per hour. To perform the conversion, you will need:

    1. The distance traveled
    2. The unit of measurement: feet, yards, miles, meters, kilometers, etc.
    3. The time in seconds

    Example

    Jill walked 30 feet in 6 seconds. To convert that to miles per hour:

    1. Write Jill's velocity as a ratio:
      30 feet in 6 seconds
    2. Write the equivalent ratio for expressing Jill's velocity in miles per hour:
      30 feet in 6 seconds equals m miles per hour
    3. Convert 1 hour to the equivalent seconds (3600):
      30 feet in 6 seconds equals m miles in 3600 seconds
    4. Divide the number of seconds in an hour (3600) by the number of seconds it took Jill to walk 30 feet.
      3600 / 6 = 600
    5. Multiply the answer in your previous step by the number of feet Jill walked:
      600 x 30 = 18,000
      That represents the number of feet Jill could walk in 1 hour at a velocity of 30 feet per 6 seconds.
    6. Convert 18,000 feet to miles by dividing it by the number of feet in a mile:
      18,000 / 5,280 = 3.4091 miles per hour
    7. You can combine the previous steps into a single formula:
      mph = 3600 / t * d / c, where
      mph = speed in miles per hour
      3600 = number of seconds in an hour
      t = time in seconds
      d = distance walked, and
      c = number of feet in a mile.

    Thinking Like a Computer Programmer

    In the previous example, you learned how to convert any velocity expressed in feet per second to miles per hour. A computer programmer would call this a function. A function is a piece of programming code that returns a value. For example, many computer programming languages have a function called NOW, which returns the time and date. Some functions need information from the user to return a value. In our velocity example, we need the time in seconds, the distance walked, and the unit of measurement for the distance.

    Here's how to build the Excel worksheet to do the conversions. We'll begin with a vertical lookup table.

    Unit of MeasurementConversion Factor
    Feet5280
    Yards 
    Meters 
    Kilometers 
    Miles 

    Hint: Remember that you can use Google to find your conversion factors.

    Next build the table to record your walkers' names, times, distances, and speed.

     ABCDEF
    8NameTimeDistanceUnitConversion FactorMPH
    9Mr. Hawthorne4.5350Feet5280=3600/B9*C9/E9
    10Anthony5.8350Feet  
    10Austin5.2750Feet  
    10Ben4.8050Feet  
    10Chaney 50Feet  
    10Christen5.6250Feet  
    10Clint6.9850Feet  
    10Drew7.9050Feet  
    10Dylan5.9650Feet  
    10Erin9.6850Feet  
    10Evan5.5350Feet  
    10Ferris5.4250Feet  
    10Grayson5.7350Feet  
    10Jayson9.5650Feet  
    10Marshall5.2550Feet  
    10Sam4.2750Feet  
    10Spenser4.5950Feet  
    10Tori8.8150Feet  
    10Zach5.5050Feet  

    The value in column E is the conversion factor for the unit of of measurement in column D. To look up the conversion factor, use Excel's VLOOKUP function. VLOOKUP stands for vertical lookup. You can use this function when your lookup values are in columns.

    The formula is =VLOOKUP(value to match,lookup table range,number of the column with the value you want to return,FALSE). This formula will be simpler if you name your lookup table range:

    1. Highlight the cells in your lookup table range. For this example, that will be the cells containing your units of measurement and their conversion factors.
    2. Choose the Insert/Name/Define menu item. Excel will display the Define Name dialog box. Give your lookup range a name. I suggest Conversion Units or ConversionFactors, spelled without spaces.
    3. Click OK to define the name. You can now refer to this range in formulas by its name, rather than by its cell addresses.

    If you name your lookup range ConversionFactors, you can use the following formula to look up the conversion factor for Anthony:

    =VLOOKUP(D10,ConversionFactors,2,FALSE)

    The 2 in this formula means that the value you want to look up is in the second column of the lookup table. The formula will take the value in cell D10 (Feet), find that value in the first column of the lookup table, and then return the corresponding value in the second column of the lookup table. The FALSE keyword in the formula means that Excel must find an exact match in the first column of the lookup table.