What is positive acceleration, negative acceleration and deacceleration?

Fig 1: Source: [3]

Acceleration is the rate of change of velocity. It is a vector that contains the direction and magnitude. We can write the formula of acceleration as below:

Source: [2]

There are two types of acceleration: average acceleration and instantaneous acceleration. Average acceleration is the ratio of the total change in velocity to the total time interval[2]. Whereas instantaneous acceleration concern about the rate of change of velocity at a particular moment in time. We are considering average acceleration as the acceleration in this article.

The rate of change of velocity in average acceleration can be defined as below:

Source: [2]

Then we can rewrite the equation of the acceleration as below:

Source[2]

Positive acceleration and negative acceleration

Normally, we call acceleration a positive acceleration when the object moves in the positive direction(left to right) and the rate of change of velocity is positive(velocity is increasing). The acceleration is negative when the object is moving in the positive direction, but the rate of change of velocity is negative(velocity is decreasing).

Fig: 2: Positive and negative acceleration in a negative direction. Source: [1]

We can also define these two acceleration when an object travels in the negative or opposite direction(right to left). In this case, the direction of the object is negative, and the rate of change of velocity is positive(velocity is increasing), then we can call it negative acceleration. It is the same as an object decreasing the velocity in a positive direction. Similarly, the rate of change of velocity decreases in the negative direction is considered positive acceleration as it implies increasing the speed in a positive direction.

Deacceleration

Acceleration and deacceleration. Source[4]

A common intuition is that deacceleration is a negative acceleration. It is true in the positive direction but not true in the opposite direction. As depicted in fig 2, deacceleration can be positive or negative acceleration, but it always has a negative value for the rate of change of velocity(velocity is decreasing).

Reference

1. https://www.youtube.com/watch?v=JTfBvzscE8c
2. https://www.khanacademy.org/science/physics/one-dimensional-motion/acceleration-tutorial/a/acceleration-article
3. https://spl-binal.blogspot.com/2016/12/e13-kinematics-acceleration.html#.YLWkg3UzaCc
4. https://isokinetics.net/index.php/2016-04-05-17-04-58/advanced/acceleration-deceleration