Should positive direction match each object's acceleration direction?

[Thomass]

Hi,
While solving homework problems, I start by defining a positive-y direction and a positive-x direction. Let's say up and to the right. Until now, I've applied this same rule to all objects in each problem, no matter the direction the object moves. But it seems I have not understood this fully.
While solving the problem for the attached picture, I had to define a positive direction up for box A, and a positive direction down for box C to get the right answer. Is the positive direction decided by which direction the object moves in constant acceleration problems like this?

 

[willem2]

The reason you have to do this is because you have chosen to keep a always positive. A consequence of this is that the force of gravity is positive for block A and negative for block C to make F=ma come out right.
Thats not how I would have done it. I would have chosen up is positive always, and the acceleration for A would be a, and the acceleration for block C would be -a.

 

[Thomass]

The reason you have to do this is because you have chosen to keep a always positive. A consequence of this is that the force of gravity is positive for block A and negative for block C to make F=ma come out right.
Thats not how I would have done it. I would have chosen up is positive always, and the acceleration for A would be a, and the acceleration for block C would be -a.

I agree! I recall doing it this way before, had forgotten all about it. Thank you :-)