JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Kinematics

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) $2 r, 3 π r$
(B) $3 π r, π r$
(C) $π r, 3 r$
(D) $3 π r, 2 r$ ✓ Correct

Answer: (D)

Solution

The ends A and B lie at opposite points of the circle, so each leg between them covers a semicircle of length

π r

. The path ABAB is three such semicircular arcs, so the distance travelled is

π r + π r + π r = 3 π r

. Displacement is the straight gap from the start A to the finish B, which is the diameter,

2 r

. The distance travelled is

3 π r

and the displacement is

2 r

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Single correct option

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