Question

directions: use your knowledge of distance - time graphs to answer the questions that follow.
part 1
comparing the speeds of the tortoise and the hare

1. what can be calculated using the distance - time graph above? explain your reasoning.
2. what does the tortoises line tell you about its speed?
3. what does the hares line tell you about its speed?

Explanation:

Step1: Recall speed - distance - time relation

Speed is calculated as $v=\frac{d}{t}$, where $v$ is speed, $d$ is distance and $t$ is time. A distance - time graph gives distance values for different time values.

Step2: Analyze Tortoise's line

The Tortoise's line is a straight - line in segments. The slope of the line in a distance - time graph represents speed. Since the slope is constant in each segment, the Tortoise has a constant speed in each non - zero slope segment.

Step3: Analyze Hare's line

The Hare's line has different slopes at different times. It has a steeper slope initially, then a zero slope (horizontal line indicating it is at rest), and then a non - zero slope again. So the Hare's speed varies; it runs fast initially, then stops, and then runs again.

Answer:

1. Speed can be calculated using the distance - time graph. Reason: Speed is the ratio of distance to time ($v = \frac{d}{t}$), and the graph provides distance values for corresponding time values. The slope of the line on a distance - time graph represents speed.
2. The Tortoise's line has constant slopes in non - zero slope segments, indicating that the Tortoise has a constant speed in each of those segments.
3. The Hare's line has varying slopes. It has a high speed initially (steep slope), then stops (horizontal line, zero speed), and then moves again with a non - zero speed (non - horizontal slope).