Final answer:
The total distance the boat traveled is 40000 meters, and the displacement of the boat is 0 meters because it returned to its original starting point.
Step-by-step explanation:
The question asks for both the total distance traveled by the boat and its final displacement. To find the distance, we simply add up the lengths of each leg of the boat's journey, regardless of direction. To find the displacement, we need to consider both the distance and direction of the boat's travel.
The boat goes east at 40 m/s for 500 seconds, then stops and turns around to go west at 50 m/s for 400 seconds. The distance traveled going east is speed × time, which is 40 m/s × 500 s = 20000 m. The distance traveled going west is 50 m/s × 400 s = 20000 m.
The total distance traveled by the boat is the sum of the distances for each leg: 20000 m + 20000 m = 40000 m.
To find the displacement, we take the difference between the eastward and westward distances since displacement is a vector quantity that depends on direction. The eastward journey results in a +20000 m displacement, and the westward journey results in a -20000 m displacement (since west is the opposite direction). Therefore, the final displacement is 20000 m - 20000 m = 0 m.