Question

under what conditions of motion the distance covered by the body is equal to the magnitude of a displacement

Answer 1

Here,
       The distance covered by the body= to the magnitude of a displacement, when
the object or the particle, move along it's axis, that too without changing it's Direction or the path, in which it is moving.
Hope it is the best.

Answer 2

Th distance covered by the body is equal to the magnitude of a displacement.It some what relates to the newton's law of motion.