Question

A sportsman runs around a circular track of radius $ r $ such that he traverses the path ABAB. The distance travelled and displacement, respectively, are:

• A. \( 2r, 3\pi r \)
• B. \( 3\pi r, \pi r \)
• C. \( \pi r, 3r \)
• D. \( 3\pi r, 2r \)

Hint:

When dealing with circular motion, remember that the displacement is the straight-line distance from start to end, and the distance is the total path length travelled.

Answer 1

The Correct Option is D

Displacement is defined as the shortest distance between the starting and ending positions. Given that the athlete completes circuits on a circular track and returns to their origin (point A), the displacement is the diameter of the circle. Consequently: \[ \text{Displacement} = 2r \] The distance covered represents the total length of the athlete's path, comprising three full circuits of the track. Hence, the total distance is: \[ \text{Distance} = 2\pi r + \pi r = 3\pi r \] Therefore, the correct response is: \[ 3\pi r, 2r \]