To find the speed of the sloth, which is the distance traveled per minute, you can use the points given in the graph.
From the points provided, we can observe:
- At \(0\) minutes, the distance is \(0\) feet.
- At \(0.5\) minutes, the distance is \(3\) feet.
- At \(1\) minute, the distance is \(6\) feet.
- At \(1.5\) minutes, the distance is \(9\) feet.
Now, we can calculate the speed (distance per time) between the different points to confirm a constant speed:
-
From \(0\) minutes to \(0.5\) minutes: \[ \text{Speed} = \frac{3 \text{ feet} - 0 \text{ feet}}{0.5 \text{ minutes} - 0 \text{ minutes}} = \frac{3 \text{ feet}}{0.5 \text{ minutes}} = 6 \text{ ft/min} \]
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From \(0.5\) minutes to \(1\) minute: \[ \text{Speed} = \frac{6 \text{ feet} - 3 \text{ feet}}{1 \text{ minute} - 0.5 \text{ minutes}} = \frac{3 \text{ feet}}{0.5 \text{ minutes}} = 6 \text{ ft/min} \]
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From \(1\) minute to \(1.5\) minutes: \[ \text{Speed} = \frac{9 \text{ feet} - 6 \text{ feet}}{1.5 \text{ minutes} - 1 \text{ minute}} = \frac{3 \text{ feet}}{0.5 \text{ minutes}} = 6 \text{ ft/min} \]
In each case, the speed of the sloth is consistently \(6\) feet per minute.
Thus, the distance a sloth travels is 6 ft. per minute.