When is acceleration positive or negative?

[XTian]

Homework Statement

In this problem, the solution says that aB= -(aA/6). But from what I know, acceleration is positive whenever an object is speeding up in the positive direction or when an object is slowing down in the negative direction. According to the problem, car B is slowing down and towards the negative direction with the assumption that going to the right is the positive direction. So why is aB= -(aA/6)? Should'nt it be aB= +(aA/6) since it is slowing down in the negative direction?

Homework Equations

N/A

The Attempt at a Solution

Maybe the sign depends on only deceleration or acceleration and not on direction in this problem? If this is the case, I'm still confused as to why the direction isn't a factor.

 

[berkeman]

But from what I know, acceleration is positive whenever an object is speeding up in the positive direction or when an object is slowing down in the negative direction. According to the problem, car B is slowing down and towards the negative direction with the assumption that going to the right is the positive direction.

You just pick the positive axis, and the sign of the acceleration is for the motion in that direction. "Slowing down in the negative direction" doesn't really make sense. Keep everything referenced to the positive axis.

 

[Orodruin]

The problem is in the solution's drawing. They have defined the position $x_A$ as increasing in the right direction but the position $x_B$ as increasing in the left direction. That can be very confusing indeed.

 

[XTian]

The problem is in the solution's drawing. They have defined the position $x_A$ as increasing in the right direction but the position $x_B$ as increasing in the left direction. That can be very confusing indeed.

After some research, I think I found what was missing in my understanding. Can you please confirm if what I currently know is right?

From what I've seen from similar problems is that they give each object their own origin. I initially thought that you only have one origin for all the object in a problem. In this problem, Car B's origin is in Xb(left is positive) hence it's acceleration is negative while it's velocity is positive while Car A's origin is in Xa(right is positive) and therefore its acceleration and velocity is positive.