JEE Main 2025 — Circular Motion Question with Solution

To determine the distance traveled and displacement of a sportsman running around a circular track, we begin by analyzing the path described as $A\to B\to A\to B$.

Displacement:

The displacement is the straight line distance from the initial point to the final point. In this case, the sportsman completes one full circle (from $A$ back to $A$) and then continues to point $B$ (which is opposite point $A$ on the circle). Therefore, the displacement is the diameter of the circle:

$\text{Displacement}=2r$

Distance:

The distance is the total path length traveled by the sportsman. Starting at $A$, he completes one full circle back to $A$, which has a circumference of:

$2\pi r$

He then runs half the circle from $A$ to $B$, which is another:

$\frac{1}{2}\times 2\pi r=\pi r$

Thus, the total distance is the circumference of the full circle plus half of another circle:

$\text{Distance}=2\pi r+\pi r=3\pi r$

In summary, the distance traveled by the sportsman is $3\pi r$ and the displacement is $2r$.