Work Energy Theorem: Delta K Calculation for Particle Moving in x Direction

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The discussion focuses on calculating the change in kinetic energy (Delta K) for a particle subjected to a net force F(x) = Cx^2 as it moves from x = L to x = 3L. A participant initially attempted to calculate Delta K by integrating the force but mistakenly replaced x with 2L, leading to an incorrect result of 2/3 CL^3. Others clarified that the correct approach involves finding the anti-derivative of the force and evaluating it over the specified interval. The proper evaluation requires substituting both limits into the anti-derivative and subtracting the results. Accurate integration is essential for determining the correct change in kinetic energy.
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A particle moving in the x direction is being acted upon by a net force F(x)=Cx^2, for some constant C. The particle moves from x initial =L to x final=3L. What is Delta K, the change in kinetic energy of the particle during that time?

I tried thih by doing the integral of F(x), replacing x with 2L (because final-initial, 3L-L). I got the answer 2/3 CL^3, and its telling me I am off by a multiplicative factor. Is this becuase I did the integral wrong, or am I missing something?

Thanks!
 
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Not sure what you did or what you mean by "replacing x with 2L". Step 1: Find the anti-derivative. Step 2: Evaluate it over the interval x = L to x = 3L. (Evaluate for x = 3L and for x = L and subtract.)
 

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