Interpret the path $A \to B \to A \to B$ on a circular track

In such standard circular-motion questions, points $A$ and $B$ are taken as diametrically opposite ends of the circular track.

• Going from $A$ to $B$ along the track means covering a semicircle.
• Length of one semicircle = half the circumference: $\frac{1}{2}(2\pi r)=\pi r$

Total distance travelled

The sportsman moves:

• $A \to B$ : $\pi r$
• $B \to A$ : $\pi r$
• $A \to B$ : $\pi r$

Therefore, total distance is $\pi r+\pi r+\pi r=3\pi r$

Displacement

Initial position = $A$

Final position = $B$

Since $A$ and $B$ are diametrically opposite points, the displacement is the straight-line distance between them, i.e. the diameter: $AB=2r$

Match with options

• Distance = $3\pi r$
• Displacement = $2r$

This corresponds to Option C.

Comparison with stored answer

Stored correct answer: C

My derived answer: C

Hence, they agree.