In classical physics, acceleration is defined as the rate of change of velocity with respect to time. However, in the context of special relativity, the concept of acceleration becomes more nuanced due to the principles of relativity, which state that the laws of physics should be the same in all inertial reference frames.
When considering two objects traveling at the same velocity relative to each other, they are in the same inertial reference frame. In this case, both objects will observe each other as being at rest or moving with a constant velocity. Since acceleration is defined as a change in velocity over time, if both objects are not experiencing any change in their relative velocities, they would perceive each other as having zero acceleration.
This observation arises from the principle of relativity, which states that the laws of physics should be the same for all observers in inertial frames of reference. In such frames, the relative motion between objects does not introduce any acceleration.
It's important to note that although both objects would agree on each other's zero acceleration, they may still experience acceleration when observed from a different inertial reference frame that is not moving at the same velocity as the objects. The concept of relativity ensures that the laws of physics remain consistent regardless of the chosen inertial frame of reference.