# Negative Velocity Positive Acceleration: Detailed Analysis

This article is a detailed analysis of how a body can have negative velocity, positive acceleration. Let’s know in detail.

Any moving body can have a negative velocity and, at the same time, positive acceleration. Both are vectors; therefore, their directions play a vital role in knowing the object’s motion. Let’s understand various examples of the several approaches of negative velocity positive acceleration.

Of course, we know what velocity is; it is the rate at which a body is moving. It is also a vector; that is, it has direction too. In the case of velocity, we take the displacement of the body rather than the distance. Now suppose a body moves from any position A to B as shown in the above figure; here, the velocity of the object is v . Now, it moves with the same velocity from B to A. Here we can see that since the direction has reversed, the velocity will become -v

That was about the velocity. Let’s look at the acceleration now. The change in velocity at regular or non-continuous time intervals is known as acceleration. It is also a vector.

Suppose a body has the initial velocity as v1 and final velocity as v2, and it moves from one velocity to another in time t. Then we have acceleration as:

a = v2-v1/t

Now two cases arise:

If v2>v1 , then the acceleration would be positive

If v2<v1, then the acceleration would be negative.

The positive acceleration means the value is increasing, whereas the negative acceleration indicates that the velocity decreases with time which is deceleration.  W know the slope of velocity time graph gives acceleration.

We have already gotten an insight into whether acceleration can be positive if velocity is negative. Let us look at some examples to understand this concept better.

We take the simplest everyday example. Suppose you are riding your bicycle from home to school. Suddenly you remember that you have forgotten your notebook, so you turn your bicycle and head toward your home. In case you have reversed the direction, initially, you were moving from home to school, but now the directions have become opposite as you are moving towards your home. So the velocity in the above situation has become negative.

Now for the same situation, let us look at the acceleration. Now that you are moving back to your home, you might be getting late for school, so you speed up. The velocity increases, i.e. your bicycle accelerates. Since now, the velocity has increased; therefore, the acceleration would be positive.

This general example makes it clear that a body can have negative velocity positive acceleration at the same time.

The above figure depicts the motion of a person. He moves from position A to B; the distance between the points is 200 m. After reaching B, the person turns around and starts moving towards A. He moves to the C point in 2 seconds. The distance between B and C is -50 m; the negative sign is because the direction of the motion has been reversed.

At point C the velocity of the person is:

velocity = Displacement/Time

v= -50/2

v = -25 m/s

The negative sign here just indicates that the body is moving in the opposite direction. Now from point C to point A, the person increased its velocity by 10 m/s and reached point A from C. Therefore, acceleration would be:

a = v2-v1/t

a = 50-25/10

a = 2.5 m s-2

So in this problem example, we have got negative velocity positive acceleration.

## What does negative velocity mean?

Velocity is the rate of motion of a body which is a vector.

The negative velocity indicates the opposite direction of a moving body. Practically, it does not indicate that the velocity has become lesser than zero. In case a body is moving from north to south and then turns to move from south to north, its velocity will become zero.

## Can acceleration be negative?

An important concept of a moving body is acceleration which also has both direction and magnitude.

Acceleration can be both negative and positive. It is the rate of change of velocity. In case the final velocity is more than the initial velocity, the acceleration becomes positive. When the initial velocity is greater in magnitude than the final velocity, it is the case of negative acceleration.

## Is it possible to have negative velocity positive acceleration?

Yes, we have already seen in this article that a body in motion can have negative velocity and, at the same time, a positive acceleration

## Is acceleration a vector?

On calculating the rate of change in velocity, we get the value of acceleration.

Acceleration can have positive as well as negative velocities. The negative value means that the velocity of the moving body is decreasing. When we press the brake of the car, the velocity reduces hence the example of negative acceleration.

## What does deceleration mean?

The acceleration is a vector that can have value with positive and negative directions.

The negative acceleration indicates the reduction in the velocity of a moving body. This negative acceleration is simply known as deceleration.

## Can a car have negative velocity?

Yes, cars can have a negative velocity.

The velocity is a vector, and hence the car’s velocity can be negative. But this negative value only indicates that the direction of the car has become opposite, and in practice, the velocity does not go below zero.

## What is zero velocity?

The velocity can have any value from negative, positive to zero.

The zero velocity is the state of the rest. At zero velocity, there has been no displacement. It indicates that the body is not moving at all.

Rabiya Khalid

Hi,  I am Rabiya Khalid, currently pursuing my masters in Mathematics. Article writing is my passion and I have been professionally writing for more than a year now. Being a science student, I have a knack for reading and writing about science and everything related to it. If you like what I write you can connect with me on LinkedIn: https://www.linkedin.com/mwlite/in/rabiya-khalid-bba02921a In my free time, I let out my creative side on a canvas. You can check my paintings at: https://www.instagram.com/chronicles_studio/