### Student Page 2.4.2 Trodding Tortoise

In Trodding Tortoise, continue to model motion with graphs and consider the race between the Hare and the Tortoise in another way. This time, from knowledge of the tortoise's speed, create a table showing the tortoise's distance from the Starting Line at various times during the race. Plot points and consider the appearance of the graph as it relates to the tortoise's speed over several time intervals. Find an equation that models the data. Finally, consider the many ways that the Tortoise's speed arises in the table, graph, and equation. In the end, define slope.

During the race between the tortoise and the hare, the fox recorded the speed at which both the tortoise and the hare were traveling. The fox observed that the tortoise plodded along at a rate of 20 meters per minute throughout the 1000-meter race.

#### 1.

##### (a)

Complete Table 2.4.2.1 indicating the distance traveled by the tortoise in the time elapsed.

Time elapsed in minutes, \(t\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

Distance traveled in meters, \(D\) | 0 | |||||||

Time elapsed in minutes, \(t\) | 10 | 15 | 20 | 25 | 30 | 35 | 640 | \(t\) |

Distance traveled in meters, \(D\) |

##### (b)

Which variable is the independent variable? Why do you think so?

#### 2.

Use the graph in Figure 2.4.2.2. For each axis, choose a scale so the graph shows the tortoise's complete race, points are easy to plot, and you use as much of the graph as possible.

##### (a)

The horizontal axis represents the independent variable. Label it using the scale you chose.

##### (b)

The vertical axis represents the dependent variable. Label it using your chosen scale.

##### (c)

Label each axis with the variable it represents.

##### (d)

Sketch a graph that represents the tortoise's progress during the race using the data in Table 2.4.2.1.

#### 3.

##### (a)

In one minute, how far did the tortoise travel? What does this number represent in terms of the tortoise's movement during the race?

##### (b)

How can you find the distance the tortoise traveled directly from the number of minutes that have elapsed since the start of the race?

##### (c)

Let \(t\) represent the elapsed time in minutes and \(D\) represent the distance in meters traveled by the tortoise. Write an equation showing the relationship between \(t\) and \(D\text{:}\)

##### (d)

Replace \(t\) in the equation in Task 2.4.2.3.c with some of the values in the table. What values did you get for \(D\) from the equation? Did the equation values for \(D\) match those in your table? Should they match?

##### (e)

How does your answer to Student Page Exercise 2.4.2.3 relate to the equation you found in Task 2.4.2.3.c?

#### 4.

##### (a)

Complete Table 2.4.2.3 for the tortoise's travels for each of the time intervals indicated.

Time Interval | Amount of time elapsed |
Change in distance during the time interval |
The tortoise's speed |
---|---|---|---|

0 to 5 minutes | |||

5 to 10 minutes | |||

10 to 20 minutes |

##### (b)

How can you find the tortoise's speed over each time interval? Explain. Enter the speed in the table.

##### (c)

Compare the tortoise's speeds for the three time intervals in the table. What do you notice?

##### (d)

Should the tortoise's speeds for each time interval be the same? Why or why not?

##### (e)

The slope of a line is the steepness of the line. What is the slope of the line that models the tortoise's movement?

#### 5.

How long does it take the tortoise to complete the race? How do you know?