Why is F=ma not applicable in this work and kinetic energy problem?

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The discussion centers on a physics problem involving work and kinetic energy, specifically a scenario where a horizontal force acts on a mass with a velocity defined as a function of position. The correct approach to find the force and work involves using the kinetic energy formula, resulting in F = 0.5m(Cx')^2. The confusion arises when attempting to apply F=ma, where the variable x' is mistakenly interpreted as a rate of change (dx/dt) instead of a final position. This misinterpretation leads to an incorrect application of the formula, highlighting the importance of understanding the context of variables in physics problems. Ultimately, the distinction between position and velocity is crucial for solving the problem accurately.
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I have been annoyed by a problem that I can't figure out. The topic is work and kinetic energy (chapter 6 in the sixth edition of physics for scientist and engineers by Paul A. Tipler). Problem 63 pg. 199

A single horizontal force F acts in the +x direction on a mass m. The intial velocity is zero, the velocity is given as a function of x v=Cx where C is a contant. If the starting point x=0 and the final point is x = x' find the force and the work.

my solution is w= .5mv^2 = .5m(Cx')^2 Therefore Fx' = .5m(Cx')^2 therefore
F=.5mx'C^2 which is the correct answer.

However, first I tried to do this

f=ma = m (dv/dt) = m[C*dx/dt] = mCx' Why is this wrong?
 
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x' in the book doesn't refer to dx/dt. It just refers to the final destination of the mass.
 
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