The distance travelled in the nth second is equal to the magnitude of displacement in the nth second IF the travelling particle DOES NOT change its direction DURING the nth second.

If, the particle changes its direction between t=n and t=n-1, then the distance travelled in the nth second is NOT the same as the magnitude of the dispacement in the nth second.



In the picture above, the first case shows the case when the particle does not change its direction during the nth second. The blue arrow represents the direction of motion of the particle in the nth second. The distance = magnitude of displacement = d in the first case.

In the second case, the particle changes direction during the nth second. Distance covered is d1 + d2 but the magnitude of displacement in the nth second is d1 - d2.