# When is acceleration positive or negative?

• XTian
In summary, the conversation discusses the confusion over the sign of acceleration in a problem involving two cars, one of which is slowing down in the negative direction. After some discussion, it is clarified that the sign of acceleration depends on the chosen positive axis and each object has its own origin in the problem. The confusion was due to the drawing in the solution, which had different origins for each car.
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?

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.

XTian said:
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.

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.

Orodruin said:
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.

## 1. When is acceleration positive?

Acceleration is considered positive when an object is speeding up, or increasing in velocity over time.

## 2. When is acceleration negative?

Acceleration is considered negative when an object is slowing down, or decreasing in velocity over time.

## 3. Can acceleration be both positive and negative?

Yes, acceleration can be both positive and negative depending on the direction of the object's motion. For example, a car can accelerate positively when it is moving forward, and then accelerate negatively when it is slowing down or reversing.

## 4. How is acceleration determined to be positive or negative?

Acceleration is determined to be positive or negative by the direction of the object's motion in relation to its velocity. If the object is moving in the same direction as its velocity, acceleration is positive. If the object is moving in the opposite direction of its velocity, acceleration is negative.

## 5. What is the difference between positive and negative acceleration?

The main difference between positive and negative acceleration is the direction of the object's motion. Positive acceleration indicates an increase in velocity, while negative acceleration indicates a decrease in velocity. Another way to think about it is that positive acceleration is associated with speeding up, while negative acceleration is associated with slowing down.

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