# Calculating Area Under a Graph with Units in Gravity-Free Space

• juju1
In summary, the conversation discusses using a graph to determine the area of one grid square and the total area under a curve to solve a problem involving a spaceship's thrust and velocity in interstellar space. The initial question is about finding the area of one grid square, which is determined by converting the units and dividing by 2. The final answer is 104670000 square meters for the total area under the curve.
juju1

## Homework Statement

[/B]
In gravity-free interstellar space, a spaceship fires its engines to speed up. The total thrust of the engines as a function of position is shown in the graph below. F on the graph represents 79 kN of thrust. The rocket's mass is 11500 kg. Note the units on the graph - kN and km! The rocket's initial velocity is 1650 m/s.

What is the area of one grid square on the graph?

What is the area under the curve?

## The Attempt at a Solution

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i tried taking 79kN and converting into N, and got 79000. Then I divided by 2 because, if you see in the image that i linked, F=79kN and F takes up 2 grid squares...i got 39500 but that was wrong!
I don't think I can solve how to find area under graph if I can't find what one grid square equals. Also there are 26.5 grid squares in total.

#### Attachments

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I am not sure what you mean by the statement,
juju1 said:
F takes up 2 grid squares.
. What made you divide by 2? Also, try answering the first question first.

If you look at the diagram, F goes up by 2.
So it would make sense to divide by 2, in order to get 1 grid

juju1 said:
What is the area of one grid square on the graph?

What is the area under the curve?

## The Attempt at a Solution

[/B]
i tried taking 79kN and converting into N, and got 79000. Then I divided by 2 because, if you see in the image that i linked, F=79kN and F takes up 2 grid squares...i got 39500 but that was wrong!
I don't think I can solve how to find area under graph if I can't find what one grid square equals. Also there are 26.5 grid squares in total.
Convert the horizontal grids to meters.

ehild said:
Convert the horizontal grids to meters.
so it would be 395000000? that seems very big...

Looks like you have an extra zero. Please make sure of that. Also, what are the units of the area that you calculated? That is the area of one grid square. Now can you find the total area under the curve?

Chandra Prayaga said:
Looks like you have an extra zero. Please make sure of that. Also, what are the units of the area that you calculated? That is the area of one grid square. Now can you find the total area under the curve?
104670000?

How did you get that number? What are the units?

## 1. How is the area under a graph calculated in gravity-free space?

The area under a graph in gravity-free space is calculated using the same method as in regular space, which is by finding the sum of all the rectangular areas formed by the graph's data points. However, in gravity-free space, the units for the area will be different, as there is no gravitational force to affect the measurements.

## 2. What units are used when calculating area under a graph in gravity-free space?

In gravity-free space, the units for area will be in square meters or square kilometers, as these are the standard units for measuring area in the metric system. Other commonly used units such as square feet or acres are not applicable in gravity-free space.

## 3. Can the area under a graph in gravity-free space be negative?

No, the area under a graph in gravity-free space cannot be negative. This is because the graph's data points, which form the rectangular areas, cannot have negative values when there is no gravitational force present. Therefore, the sum of these positive values will always result in a positive area.

## 4. How does the absence of gravity affect the calculation of area under a graph?

The absence of gravity does not affect the calculation of area under a graph, as the method remains the same. However, the units for the area will be different, as explained earlier. Additionally, in gravity-free space, the graph's shape may be distorted due to the lack of gravitational pull, but the area calculation itself will not be affected.

## 5. Can the area under a graph in gravity-free space be used to measure volume?

No, the area under a graph in gravity-free space cannot be used to measure volume. While both volume and area are measurements of space, they are not interchangeable. Volume measures the amount of space an object occupies, while area measures the size of a surface. Therefore, the area under a graph in gravity-free space cannot be used to determine an object's volume.

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