The scenario you've described is a theoretical situation that cannot occur in physical reality. It violates the fundamental principles of classical mechanics. Let me explain why:
Acceleration is defined as the rate of change of velocity. If an object has zero velocity, it means it is not moving. In such a case, the concept of acceleration loses its meaning because acceleration describes how velocity changes over time. Without any velocity, there is no change to measure.
Moreover, an infinite acceleration implies an instantaneous change in velocity, which is not possible for physical objects governed by classical mechanics. Objects in the real world have finite masses and are subject to physical constraints. The laws of classical mechanics govern their motion, and they cannot undergo instantaneous changes in velocity or experience infinite accelerations.
If we encounter situations where the acceleration appears to be infinite, it usually indicates that our understanding or model is incomplete or there are extreme simplifications made in the theoretical scenario. It might require the application of more advanced theories, such as those in the realm of relativistic physics or quantum mechanics, to properly describe and understand such phenomena.
In summary, the concept of an object having zero velocity and simultaneously experiencing infinite acceleration in opposite directions is not consistent with classical mechanics or physical reality.