*Even when the velocity is negative, acceleration can be positive. Let us know about the negative velocity positive acceleration graph. *

**By plotting the graph of velocity-time, we get the acceleration as the slope. The negative sign of the velocity infers that the object’s motion is in the opposite direction. The velocity does not actually go below zero.**

If the object moves in the opposite direction, then its velocity is represented by a negative sign. For example, if a boy is going to the market with velocity v, then from coming back from the market to home with the same speed, the velocity will become -v.

Since velocity is negative, therefore, the acceleration can also be negative. The positive acceleration gives the rate of increasing velocity. At the same time, the negative acceleration implies the rate of decreasing velocity.

We have already seen that a body can have negative **velocity** positive acceleration. Let’s take the example we have mentioned above; while coming back from the market, the velocity is negative. Now, if the boy increases his velocity to reach home faster, the acceleration is positive.

Let us know how to plot negative velocity positive acceleration graphs.

Suppose a man was travelling from his home to his office by car. But due to some reason, he reversed his car and is now moving back to his home. The above table shows us the motion of the car. The negative sign is here to infer that the direction of the object is in the opposite direction.

We take velocity components on the y-axis, and time is represented on the x-axis. Since velocity is negative, therefore, we take it on the negative y-axis.

The next step is to plot a negative velocity positive acceleration graph. For this, we take the points from the above table as A(1, -100), B (2, -80), C(3, -60), D(4, -40).

After plotting the graph, we joined all the points and got the slope. We know by calculating the slope of the velocity-time graph, we get to know about the acceleration of the object. On moving, from left to right, the slope is moving upwards, so it is obvious that it is positive, i.e. positive acceleration.

Now moving on forward, let’s find the acceleration from the graph. Take any two points on the graph P and Q and plot their coordinates. Now substitute these points in the slope formula slope = y_{2}-y_{1}/x_{2}-x_{1}

We know that the slope of the velocity-time graph gives acceleration; therefore, acceleration for the above graph is, which is positive.

Now the negative velocity graph can be of two types. First, the negative velocity positive acceleration graph and the other one gives negative velocity negative acceleration.

The negative velocity positive acceleration graph is as shown in the above figure. The velocity is decreasing, and that too is in the negative direction. And if we move from left to right, the slope is going upward; that is, acceleration is positive.

The negative velocity negative **acceleration** is as shown in the above figure. Here we can see that velocity is negative and increasing in the opposite direction. And the slope moves downward; therefore, acceleration is negative.

So, from the above discussion, we are able to understand the negative velocity positive acceleration graph.

**Frequently Asked Questions (FAQs)**

**Can acceleration be negative?**

Yes, the acceleration can be a vector as well because it is a vector.

**The negative acceleration indicates that the rate of velocity of the particular object is decreasing. The negative acceleration is also termed deceleration or retardation. **

**is negative velocity positive acceleration graph possible? **

Yes, the acceleration can be negative or positive when the velocity is negative.

**For example, a cat is moving down the tree, then the velocity is negative, but it increases to its speed, then the acceleration becomes positive. Therefore negative velocity and positive acceleration are possible. **

**Where is acceleration positive on the velocity-time graph?**

From the slope of the velocity-time graph, we get the value of acceleration.

**Therefore to calculate the acceleration, we find the slope of the graph. If the slope is moving upwards when going from left to right of the graph, then the acceleration is positive**.

**How to find acceleration from a velocity-time graph?**

The graph of velocity and time represents the motion of a moving object on the graph.

On the velocity-time graph, we represent the velocity on the y-axis and the time on the x-axis. Thus slope is calculated by:

slope =Δy/Δx = y_{2}-y_{1}/x_{2}-x_{1}

**The slope gives the value of the acceleration of the moving body. **

**Does positive velocity mean positive acceleration?**

No, the positive velocity doesn’t need to mean positive acceleration.

**For instance, if a person is driving a car at 80 km/hr but after moving to some distance, the traffic increases and he, therefore, decreases its velocity to 50 km/hr. Since the velocity has decreased, it shows negative acceleration but positive velocity. **

**What is retardation or deceleration? **

Retardation and deceleration mean exactly the same thing.

**Retardation and deceleration are the same as negative acceleration. It indicates the velocity of the moving body is decreasing with time**. **The slope of the negative acceleration is downward that is on moving from left to right it moves downwards.**

**What is an example of positive acceleration?**

Positive acceleration is explained as the increase in the velocity of the object with time.

**In case you are riding a bicycle and racing with your friend. Now to win the race, you accelerate the bicycle and its velocity increases. The acceleration would be positive; that is, it would be increasing. The slope of positive acceleration moves in the upward direction.**