Referring to Figure 1.10 in Chapter 1 of the text (reproduced below), compare the magnitudes of the average accelerations for Hare and the Tortoise.

Question

BlackTom AI · Accepted Answer

The task asks us to compare the magnitudes of the average accelerations for Hare and the Tortoise using the figure provided.

First, recall what average acceleration means: it is the change in velocity over a time interval, not directly a change in position. To determine average acceleration from a graph, you would typically need either a velocity–time graph or data that allows you to compute velocity at multiple times and then take a time-difference of those velocities.

Second, examine what is given: the figure is a distance–time plot (position vs. time) showing the motion of two runners over time. A distance–time plot tells you about speeds (slopes) at various segments, but it does not directly provide velocities at the endpoints of the interval or how those velocities change over time unless you extract slope information and know the corresponding time intervals precisely.

Therefore, inferring the average accelerations of Hare and Tortoise from this distance–time figure alone is not straightforward. You would need to know the velocities (slopes) at the start and end of the interval or have a velocity–time representation to compute the change in velocity over the total time.

Analyzing the single provided option:
- Option: "The Tortoise and the Hare have the same average acceleration" 
  Why this is not necessarily correct: without explicit velocity data or a velocity–time curve, asserting equal average accelerations for both creatures is unwarranted. The tortoise and hare move at different speeds and likely change speeds differently over time, so their velocity changes (and thus their average accelerations) are not guaranteed to be the same. Additionally, a distance–time plot can show periods of rapid vs. slow movement, but it does not automatically equate their average accelerations.

In summary, given only the distance–time figure, you cannot robustly conclude that the average accelerations are equal; the statement is not supported. The lack of velocity data means the claim is unfounded based on the information provided, and the conclusion would depend on additional details about how each animal’s speed changes over the interval.

Phys_2305_O'Donnell_Fall2025 Quiz 01 - Chapters 1 & 2, Chapter 3 (3.1-3.2)

Referring to Figure 1.10 in Chapter 1 of the text (reproduced below), compare the magnitudes of the average accelerations for Hare and the Tortoise.

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