In the first case a) the magnitude of the displacement and the distance are not the same .
Explanation : You would be knowing that Displacement is a vector quantity and determines the magnitude and the direction as well , here in the athlete case he completes one lap i.e he comes back to its position from where he started sop the while running the direction at each point was different so the displacement was at each point was also different and when he reached the original position the direction was the same hence the angle would 0 or 360 degree. Displacement means the change in quantity in the initial position.He came back from where he started and the displacement means the length of the straight line path of its curved path or in simple words the length of the line joining the initial position and the final position.Here the initial position is same as the final position so there is no straight line drawn to measure its displacement so the displacement is zero(0). And distance being a scalar quantity which means how much the athlete has walked or traveled(traversed) from its initial position(it is not the change in its initial position) so here the distance would be the length of the one lap path which the athlete has ran.
Conclusion : The magnitude of the distance and the displacement are not the same.Displacement is zero and the distance is the length of the path of one lap.
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