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:

- 60 mph
- 60 miles/hour
- 60 miles:1 hour

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.

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

- 4 girls per 14 boys
- 4:14

You can also reduce this ratio to:

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:

- 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?
- 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?
- 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.
- The distance traveled
- The unit of measurement: feet, yards, miles, meters, kilometers, etc.
- The time in seconds
- Write Jill's velocity as a ratio:

- Write the equivalent ratio for expressing Jill's velocity in miles per hour:

- Convert 1 hour to the equivalent seconds (3600):

- Divide the number of seconds in an hour (3600) by the number of seconds it took Jill to walk 30 feet.

3600 / 6 = 600 - 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. - 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 - 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. - 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.
- 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.
- Click OK to define the name. You can now refer to this range in formulas by its name, rather than by its cell addresses.

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

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

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 Measurement | Conversion Factor |
---|---|

Feet | 5280 |

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.

A | B | C | D | E | F | |
---|---|---|---|---|---|---|

8 | Name | Time | Distance | Unit | Conversion Factor | MPH |

9 | Mr. Hawthorne | 4.53 | 50 | Feet | 5280 | =3600/B9*C9/E9 |

10 | Anthony | 5.83 | 50 | Feet | ||

10 | Austin | 5.27 | 50 | Feet | ||

10 | Ben | 4.80 | 50 | Feet | ||

10 | Chaney | 50 | Feet | |||

10 | Christen | 5.62 | 50 | Feet | ||

10 | Clint | 6.98 | 50 | Feet | ||

10 | Drew | 7.90 | 50 | Feet | ||

10 | Dylan | 5.96 | 50 | Feet | ||

10 | Erin | 9.68 | 50 | Feet | ||

10 | Evan | 5.53 | 50 | Feet | ||

10 | Ferris | 5.42 | 50 | Feet | ||

10 | Grayson | 5.73 | 50 | Feet | ||

10 | Jayson | 9.56 | 50 | Feet | ||

10 | Marshall | 5.25 | 50 | Feet | ||

10 | Sam | 4.27 | 50 | Feet | ||

10 | Spenser | 4.59 | 50 | Feet | ||

10 | Tori | 8.81 | 50 | Feet | ||

10 | Zach | 5.50 | 50 | Feet |

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:

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.