When there is no air resistance, objects of different masses dropped from rest will fall with equal accelerations and with equal displacements. This is because in the absence of air resistance, the only force acting on the objects is gravity, which is the same for all objects regardless of their mass. Therefore, all objects will experience the same acceleration due to gravity and will fall with the same rate. Additionally, since the objects are dropped from rest, they all start at the same initial position and therefore will have the same displacement at any given time.