Eight times
Explanation
Motion along a polygonal track consists of straight-line motion along the sides of the polygon, with abrupt changes in direction occurring at the vertices (corners) to maintain the path.
Analysis:
- A regular octagon is a closed geometric figure possessing eight equal sides and eight vertices.
- An athlete running on this track moves in a straight line along one side. Upon reaching a vertex, the athlete must turn to align with the subsequent side.
- To complete one full lap, the athlete must traverse all eight sides and negotiate all eight corners.
- Therefore, the direction of motion changes exactly eight times, corresponding to the eight vertices of the octagon.
Key Takeaway:
For an object moving along a closed regular polygonal path with n sides, the direction of motion changes n times in a single complete revolution.