Motion in a Straight Line · Question 15

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

1. r, 3r
2. 2r, 3 r
3. 3 r, 2r
4. 3 r, r

Answer

(3) 3 r, 2r

Solution

A and B are the ends of a diameter, so each move A → B or B → A covers half the circumference.

Path ABAB = A → B → A → B = 3 half-circles

Distance = 3 r = 3 r

The sportsman starts at A and stops at B

Displacement = AB = diameter = 2r

Answer: (3)