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1. The problem statement, all variables and given/known data

A net force along the x-axis that has x-component Fx=−12.0N+(0.300N/m2)x2 is applied to a 3.20kg object that is initially at the origin and moving in the -x-direction with a speed of 8.60m/s

What is the speed of the object when it reaches the point x = 9.00m ?

2. Relevant equations

F=ma
.5mv^2=Ke

3. The attempt at a solution

Not really sure where to go with this. I can find, using the basic N2 formula, that the acceleration of the object changes according to the Fx equation given divided by mass, giving an acceleration of 3.84 m/s at x=9.00m.

However, I’m not sure how to find how far the object travels in the -x direction. Is the acceleration I have calculated at x=9 instantaneous or average? I’m not sure how to apply the kinetic energy to this problem either. Initial energy is 118.34 J, however, as the force applied is changing, isn’t the energy going to continuously change as well? We can’t apply any sort of energy conservation to this if that is the case.

I can understand that I need to find how far the object travels in the -x direction, then calculate the change in velocity over the distance it travels back toward the x=9 mark… I’m just lost as to how to get there…