To find the instantaneous speed at 2 seconds from the graph described, you need to analyze the slope of the position vs. time graph at that point.
From the description:
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From 0 seconds to 4 seconds, the line goes from (0,0) to (4,12). This indicates a constant velocity during this period.
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The slope (speed) can be calculated as follows:
\[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{12, \text{m} - 0, \text{m}}{4, \text{s} - 0, \text{s}} = \frac{12, \text{m}}{4, \text{s}} = 3, \text{m/s} \]
At 2 seconds, the position is increasing linearly, so the instantaneous speed at 2 seconds is also 3 m/s.
Average Speed Over the Entire Trip
To find the average speed over the entire trip, you can use the formula:
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]
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The total distance traveled is from 0 meters to 12 meters (and then back to 0 meters), which means:
- Distance from 0 to 12 meters = 12 meters
- Returning back from 12 meters to 0 meters = 12 meters
- Total distance = 12 m + 12 m = 24 m.
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The total time for the entire trip is from 0 seconds to 12 seconds, which is 12 seconds.
Now, we can calculate the average speed:
\[ \text{Average speed} = \frac{24, \text{meters}}{12, \text{seconds}} = 2, \text{m/s} \]
So, the average speed over the entire trip is 2 m/s.
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