Question

1. describe the hares speed during the period of time between five and twenty minutes?
2. use the speed formula to compare and contrast the speeds for both the tortoise and the hare in the first five minutes. show your work!
3. use the speed formula to compare and contrast the speeds for both the tortoise and the hare in the final five minutes. show your work!
4. use the speed formula to compare and contrast the speeds for both the tortoise and the hare for the 25 - minute period of time. show your work!
5. for the previous three (5 - 7) questions it was necessary to use the formula to help you compare and contrast the speeds of the tortoise and the hare. explain how you could compare and contrast their speeds just by looking at the distance - time graph, without performing calculations.
6. provide a detailed summary of the events that took place while the tortoise raced the hare.

Explanation:

Step1: Recall speed formula

The speed formula is $v = \frac{d}{t}$, where $v$ is speed, $d$ is distance, and $t$ is time.

Step2: For question 5 - First five minutes

Let the distance covered by the Tortoise in first 5 minutes be $d_{t1}$ and by the Hare be $d_{h1}$. Then the speed of the Tortoise $v_{t1}=\frac{d_{t1}}{5}$ and the speed of the Hare $v_{h1}=\frac{d_{h1}}{5}$. Compare the values of $d_{t1}$ and $d_{h1}$ to contrast the speeds.

Step3: For question 6 - Final five minutes

Let the distance covered by the Tortoise in the final 5 minutes be $d_{t2}$ and by the Hare be $d_{h2}$. Then the speed of the Tortoise $v_{t2}=\frac{d_{t2}}{5}$ and the speed of the Hare $v_{h2}=\frac{d_{h2}}{5}$. Compare the values of $d_{t2}$ and $d_{h2}$ to contrast the speeds.

Step4: For question 7 - 25 - minute period

Let the distance covered by the Tortoise in 25 minutes be $D_{t}$ and by the Hare be $D_{h}$. Then the speed of the Tortoise $V_{t}=\frac{D_{t}}{25}$ and the speed of the Hare $V_{h}=\frac{D_{h}}{25}$. Compare the values of $D_{t}$ and $D_{h}$ to contrast the speeds.

Step5: For question 8 - Analyzing graph

The steeper the slope of the distance - time graph, the greater the speed. If the slope of the Tortoise's graph is steeper than the Hare's at a certain time interval, the Tortoise is faster in that interval and vice - versa.

Step6: For question 9 - Event summary

In the beginning, the Hare is much faster and gets ahead quickly. Then the Hare may stop (rest or play) for a while. During this time, the Tortoise, moving at a steady slow pace, gradually catches up. Eventually, the Tortoise may overtake the Hare and win the race.

Answer:

For question 5: Calculate speeds using $v=\frac{d}{t}$ and compare.
For question 6: Calculate speeds using $v=\frac{d}{t}$ and compare.
For question 7: Calculate speeds using $v = \frac{D}{T}$ and compare.
For question 8: Steeper slope means higher speed on distance - time graph.
For question 9: Hare starts fast, may stop, Tortoise moves steadily and may overtake.