First, we know acceleration is a quantity which has magnitude, unit, direction and obeys the laws of vector addition. That is, the physical quantity acceleration is a vector quantity.

For any vector quantity, if it travels only along one particular direction (one – dimensional), it can be either in North or south or east or west. Also, it can be upwards or downwards or rightwards or leftwards. So, in order to indicate direction, cartesian signs were used in physics to bring standard and ease of physics language usage. Hence, cartesian sign conventions are used in physics to simplify the language of physics.

Therefore, if acceleration is positive, it can be of only one meaning. It is acting either in +X or +Y direction.

Misconception:

The sign positive, since we often used in mathematics as a fundamental arithmetic operation, students easily relate to increase in something or adding.

But, in physics one needs to understand we are not dealing with pure numbers we are dealing with the physical quantities. So, the meaning of signs used in a quantity changes based on the nature of quantity dealt such as scalars or vectors.

For vector quantities dealt in one direction, sign only indicates the direction in which the quantity acts.

Then, when to argue that speed of the body increases?

Let’s say you are driving a cycle on the road. That is, you are making the cycle to move in forward direction with a particular velocity. If suddenly imagine, the wind blows in opposite direction. That is, the wind is trying to push you in backward direction opposing your direction of motion. Thus, wind is trying to change your velocity in backward direction, hence wind applies backward acceleration to the cycle. Therefore, the cycle slows down when velocity and acceleration act opposite to each other.

Let’s suppose wind is blowing in the same direction of motion of the cycle. That is, wind is trying to change your direction of velocity along the original direction of cycle. Hence, wind applies forward acceleration to the cycle. Therefore, the cycle speeds up when velocity and acceleration act in the same direction.

Conclusion:

In order to know, the body will speed up or slow down, we need two information such as both the direction of velocity as well as direction of acceleration.

Hence, only with the direction of acceleration such as ‘positive acceleration’ or ‘negative acceleration’ we cannot say that the body will speed up or slow down.

Therefore, one needs to understand that there can be chance of increase in speed of a body with negative acceleration if velocity also act in negative direction and can be chance of decrease in speed of body with positive acceleration with velocity act in negative direction.

Positive and negative simply indicates only the direction for the vector quantities!