Explain clearly, with examples, the distinction between :
(a) magnitude of displacement (sometimes called distance) over an interval of time,
and the total length of path covered by a particle over the same interval
The magnitude of displacement over an interval of time is the shortest distance (which is a straight line) between the initial and final positions of the particle.
The actual path length covered by the particle in a given interval of time is the total length of the path covered by the particle.
Consider, for example, a particle moves from point A to point B and then, comes back to a point, C taking a total time t.
Displacement of the particle = AC
Total path length = AB + BC
Magnitude of displacement can never be greater than the total path length. However, in some cases, both quantities are equal to each other.