The positive acceleration when the acceleration is in the direction of motion of object. The negative acceleration can be in two types. First is the one when an object is in motion and it slows down and the direction of the acceleration is in the negative direction. The second is the one when the direction of the acceleration is in the direction of velocity and the object increases its speed. Letâ€™s discuss the negative acceleration, its graph representation, and some more examples based on it.

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Before dealing with negative acceleration, we are supposed to know what is acceleration? The process of changing the velocity is called the acceleration of the motion.

**The basic definition of the acceleration is that, it is ratio of the change in velocity to the time taken.**

**a = $\frac{[v_{f} - v_{i}]}{[t]}$****,**

where,** **

V_{f} is the final velocity of the object,

V_{i} is the initial velocity of the object and

**t** is the time needed for this change of velocities.

where,

V

V

As we said the effect of acceleration is to change the velocity of the moving object. The change needs not always be an increase. Suppose the situation changes at any time, i.e., you see a traffic signal ahead with a red light or you find a
congested traffic ahead. What you do is remove your foot from the
accelerator and shift it to the brakes and press that. What does the
brakes do? It reduces the velocity of your car. In fact the name brake
is derived from the term breaking the speed. This is called the deceleration meaning the negative acceleration.

It is a convention that an acceleration is defined as the final velocity minus initial velocity over the time taken. When you are reducing the velocity, which happens in negative acceleration or deceleration, obviously the difference in the velocities is a negative quantity and hence the acceleration becomes a negative ratio. Thus, the reduction in velocity automatically gives you a negative acceleration.

Therefore, the acceleration can be**Negative**.

Therefore, the acceleration can be

Positive Acceleration :

If the velocity of an object increases, then the object is said to be moving with positive acceleration.

- A ball rolling down on an inclined plane.
- When you are driving you find the road is clear and for obvious reasons of saving the time you increase the speed of your car. This is called a positive acceleration.

In other words, a positive acceleration means increasing the speed within a time interval, usually very short interval of time.

Negative Acceleration :

If the velocity of an object decreases, then the object is said to be moving with negative acceleration. Negative acceleration is also known as retardation or deceleration.

- A ball moving up an inclined plane.
- A ball thrown vertically upwards is moving with a negative acceleration as the velocity decreases with time.

We have explained that a negative acceleration occurs when the velocity of an object gets reduced over a period of time. That means, the slope of the velocity function is negative. It may be noted that, here, we do not mean that the velocity itself becomes negative but the velocity is decreasing and there by the slope of the velocity function is negative. As per the concept of calculus the derivative of the function is negative.

The Concept of Negative acceleration can be better understood when we see a Negative acceleration graph. Let us recall that a velocity is the slope of a displacement graph and an acceleration is the slope of a velocity graph.

The Concept of Negative acceleration can be better understood when we see a Negative acceleration graph. Let us recall that a velocity is the slope of a displacement graph and an acceleration is the slope of a velocity graph.

The above diagram shows the graphs of velocity and acceleration of an object. The object goes with an increase in velocity with a constant positive acceleration up to a point **P** and then goes with an decrease in velocity with a constant negative acceleration from point** P**. The acceleration graph drops down to a negative value at point **P**.

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