To find the average rate of change in the dolphin's position, we need to calculate the total change in position and divide it by the total time taken.
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Determine the total change in position:
- The dolphin rose to 3.5 m above the water. We can represent this as +3.5 m.
- Then, it dove 10 m below the water, which we can represent as -10 m.
To find the total change in position, we add these two values together:
\[ \text{Total change in position} = 3.5 , \text{m} + (-10 , \text{m}) = 3.5 , \text{m} - 10 , \text{m} = -6.5 , \text{m} \]
This indicates that the final position is 6.5 m below the surface of the water.
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Determine the total time taken: The total time taken for this change in position is given as 12.5 seconds.
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Calculate the average rate of change: The average rate of change is found by dividing the total change in position by the total time taken:
\[ \text{Average rate of change} = \frac{\text{Total change in position}}{\text{Total time}} = \frac{-6.5 , \text{m}}{12.5 , \text{s}} \]
Calculating this gives:
\[ \text{Average rate of change} = -0.52 , \text{m/s} \]
Thus, the average rate of change in the dolphin's position is -0.52 m/s when rounded to the nearest hundredth. The negative sign indicates that the dolphin's overall movement was downward relative to the starting surface level of the water.
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