Person A is in car A and person B is in car B. These people don't know if their car is moving (i.e. there is no scenery and their engines don't vibrate or make noises). Car A is stopped and car B is moving with a velocity v. Person A thinks that car B is moving with a velocity v while person B thinks that car A is moving with a velocity of -v. Except for the fact that I said that car B was the one moving, it would be impossible to tell, correct? Does it work the same way with acceleration? Is it possible to know whether car A is accelerating with an acceleration a or car B is accelerating with an acceleration -a? If so, why is that different from how it works with velocity (I'd prefer more of a mathematical/scientific reason, not just "because that is how physics works")?