Motion in a straight line

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;
(b) magnitude of average velocity over an interval of time, and the average speed
over the same interval. [Average speed of a particle over an interval of time is
defined as the total path length divided by the time interval]. Show in both (a)
and (b) that the second quantity
is either greater than or equal to
the first. When is the equality sign
true ? [For simplicity, consider
one-dimensional motion only].