# Why do you divide by 2 get get the area under a linear graph?

• Mar 8th 2010, 04:58 PM
Masterthief1324
Why do you divide by 2 get get the area under a linear graph?
This question applies to finding the amount of work done.
Let's say I did an experiment where I pulled a spring. Let 'x' be the distance I pulled the string and f(x) be the force required to pull the ptring.

The result of the experiment is:
x (Meters):1,2,3,4,5,6,7,8,9,10
f(x) (Newtons):2,3,4,5,6,7,8,8,10,11

If I was to graph the data, I would get a linear line. To get the total amount of work done, wouldn't I just have to multiply the final distance
by the final amount of force (required to pull the spring)?
After all W = Force * Distance.

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If I were to graph the CHANGE in distance (delta X) against the amount of force required, would I still have to divide by 2?
• Mar 9th 2010, 12:47 AM
earboth
Quote:

Originally Posted by Masterthief1324
This question applies to finding the amount of work done....

1. To answer the question in the headline: The area in question is a triangle with it's base on the x-axis and the height parallel to the y-axis.

2. The area of every triangle is half of a rectangle:

$a_\Delta = \frac12 \cdot base \cdot height$

That's where the division by 2 comes from.