# Drawing Kinematic Graphs for Negatively Accelerating Velocity-Time

• dranseth
In summary, to draw the acceleration-time graph for a velocity-time graph that is negatively accelerating, you would need to find the slope of the velocity-time graph at each point and graph it onto a new graph. The acceleration graph will not be linear, as the slope of the velocity-time graph is constantly changing. At the point where the slope of the velocity-time graph is zero, the acceleration becomes negative and the graph would show a linear line below the x-axis.
dranseth

## Homework Statement

If we have a velocity-time graph that is negatively accelerating, how would we draw the graph for the acceleration time graph? Would we draw it below zero because it is negatively accelerating (negative number).

The picture of the graph is attached.

## The Attempt at a Solution

I drew a linear line below the x-axis to show that the acceleration was negative.

The value of the acceleration at an instant is the value of the slope of the velocity time curve at that instant. Based on that, you can see that the acceleration starts out positive, but it is not constant. The velocity is increasing at an ever decreasing rate, which means that the acceleration is decreasing. At the point where the slope of the v-t graph is zero, velocity hits a maximum, then starts decreasing. This is the point at which the acceleration makes the transition from positive to negative.

so the line for the acceleration-time graph would be linear with a negative slope, then at 0 for a bit when the velocity is constant, then there would be another linear line below the x-axis with a negative slope?

The graph of the acceleration is the graph of the derivative of the v-graph. Find the slope at each second and graph it onto a new graph. The a-graph is not linear.

Yeah, I never said that it was linear because you can't tell that by inspection. I just said that it was decreasing, that it starts out positive, crosses zero, and becomes negative.

## 1. How do you draw a kinematic graph for negatively accelerating velocity-time?

To draw a kinematic graph for negatively accelerating velocity-time, you will need to plot the velocity on the y-axis and time on the x-axis. The slope of the graph will represent the acceleration, which will be negative for a negatively accelerating object. The graph will start with a positive velocity and then decrease in a smooth, curved line.

## 2. What is the difference between a positively and negatively accelerating velocity-time graph?

The main difference between a positively and negatively accelerating velocity-time graph is the direction of the slope. In a positively accelerating graph, the slope will be positive, indicating an increase in velocity over time. In a negatively accelerating graph, the slope will be negative, indicating a decrease in velocity over time.

## 3. How can you determine the acceleration from a negatively accelerating velocity-time graph?

The acceleration can be determined by finding the slope of the graph. In a negatively accelerating graph, the slope will be negative, and the magnitude of the slope will represent the acceleration. You can also calculate the acceleration by dividing the change in velocity by the change in time.

## 4. Is it possible for an object to have a negative acceleration and still be moving forward?

Yes, it is possible for an object to have a negative acceleration and still be moving forward. This can happen when an object is slowing down, but still moving in the positive direction. For example, a car decelerating while moving forward will have a negative acceleration.

## 5. What does the area under a negatively accelerating velocity-time graph represent?

The area under a negatively accelerating velocity-time graph represents the displacement or distance traveled by the object. This can be calculated by finding the area of the triangle formed by the x and y-axis and the curve of the graph. The units for the area will be in meters or feet, depending on the units used for the velocity and time.

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