A dolphin jumped above the surface of the water it reached the altitude of 3.5 m above the surface of the water and then dough 10 M below the surface of the water it went from his highest point above the water to its lowest depth in 12.5 seconds interpret the question to describe the average rate of change of dolphins position.

Answer 1

To find the average rate of change of the dolphin's position over the total time of 12.5 seconds, we can follow these steps:

1. Determine the initial and final positions:

   • The highest point above the water is +3.5 meters (above the surface).
   • The lowest point below the water is -10 meters (below the surface).

2. Calculate the change in position:

   • The change in position (\(\Delta y\)) from the highest point to the lowest point can be calculated as: \[ \Delta y = \text{final position} - \text{initial position} = -10 , \text{m} - 3.5 , \text{m} = -13.5 , \text{m} \]
   • This result indicates that the dolphin moved 13.5 meters downward (since it's a negative change in position).

3. Determine the time taken:

   • The time (\(\Delta t\)) taken for this movement is 12.5 seconds.

4. Calculate the average rate of change:

   • The average rate of change (\(v_{avg}\)) of the dolphin's position can be found using the formula: \[ v_{avg} = \frac{\Delta y}{\Delta t} \]
   • Plugging in the values: \[ v_{avg} = \frac{-13.5 , \text{m}}{12.5 , \text{s}} = -1.08 , \text{m/s} \]

Interpretation: The average rate of change of the dolphin's position over the time interval of 12.5 seconds is approximately -1.08 meters per second. The negative sign indicates that the average movement is downward, meaning the dolphin was descending into the water during this time period.