How to Graph Potential Energy from Force Fx Along the x-axis?

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To graph the potential energy from the force exerted on a particle along the x-axis, the force function must be integrated piecewise due to its non-constant nature. For the interval from 0 to 0.5 meters, the force is linear, leading to a potential energy function of U = 2x^2. From 0.5 to 1 meter, the force changes, resulting in a potential energy function of U = -2x^2 + 4x - 1. Beyond 1 meter, since the force is zero, the potential energy remains constant and should not revert to zero. The area under the force-displacement curve is critical for accurately determining the potential energy across these intervals.
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bestchemist said:
Sooo
∫F= 0
so U = 0x +k
so U =1?
looks good. Remember the check I mentioned, U at x = 1.1 is the Area under the force-displacement curve between x= 0 and x = 1.1. But you still need to graph it as the problem asks.
 

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