Question

under what condition will the magnitude of displacement be equal to the distance travelled by an object

Answer 1

Distance covered is only ever equal to the magnitude of displacement if the direction component of the object's velocity is constant. That is, as long as the object travels in a straight line, without doubling back, will distance = displacement.

Answer 2

if the direction component of the displacement is constant then the magnitude of displacement is equal to the distance covered.
i.e. if the boidy continues its motion in one direction without any backward movement then the final displacement will be equal to the distance covered.