Final answer:
The boat's acceleration while it travels 22.0 m is approximately 0.39 m/s^2.
Step-by-step explanation:
The magnitude of the boat's acceleration can be calculated using the equation:
acceleration = (final velocity - initial velocity) / time
Given that the boat travels 22.0 m, and the velocity reduces from 12.5 m/s to 3.5 m/s, we can calculate the time using the equation:
displacement = (initial velocity + final velocity) / 2 * time
Using these equations:
acceleration = (3.5 m/s - 12.5 m/s) / time
22.0 m = (3.5 m/s + 12.5 m/s) / 2 * time
Substituting the second equation into the first, we can solve for the time:
acceleration = (3.5 m/s - 12.5 m/s) / ((3.5 m/s + 12.5 m/s) / 2 * time)
Simplifying, we find that the magnitude of the boat's acceleration is approximately 0.39 m/s2.