Final answer:
Two objects, one with constant velocity and another accelerating, can have the same average velocity and displacement if they start and finish at the same places in the same amount of time. Their instantaneous velocities may converge at specific points but are not generally equal.
Step-by-step explanation:
The question deals with understanding the concepts of displacement, average velocity, and instantaneous velocity in the context of two objects: one moving with a constant velocity and the other accelerating. Option (a) indicates that it is not possible for two objects to have the same displacement, average velocity, and instantaneous velocity at the same time if one is accelerating and the other is at a constant velocity. However, considering that average velocity is the total displacement divided by the total time of travel, two objects can indeed have the same average velocity if they start and end at the same point in the same amount of time, regardless of their individual motions at various times during the journey.
For example, if Object A moves with a constant velocity, it covers equal displacements in equal intervals of time. In contrast, Object B might accelerate and therefore cover different displacements in equal intervals of time, but it could have a period of high acceleration followed by deceleration leading it to arrive at the same endpoint at the same time as Object A. Here, both objects would share the same average velocity and displacement by virtue of starting and ending at the same points at the same times, but their instantaneous velocities may only be equal at one or more specific points in time.