How can a particle experiencing a force be solved using work and energy?

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To solve for the velocity of a particle experiencing a force, the work-energy theorem can be applied. The work done on the particle can be calculated using the integral of force over distance. This approach allows for determining the change in kinetic energy, which can then be used to find the final velocity. The initial conditions, including mass and initial velocity, are crucial for setting up the equations. Ultimately, using these principles leads to the solution of 6.8 m/s for the particle's final velocity.
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Homework Statement


A 600 g particle moving along the x-axis experiences the force shown in the figure . The particle's velocity is 2.0 m/s at x = 0\:{\rm{ m}}.

11.EX15.jpg


Homework Equations


The Attempt at a Solution


To be completely honest, I don't have a clue on how to even start this problem. I tried to use the 1D kinematic equations, but that didn't result in anything useful because I don't know the acceleration. I tried to find the acceleration with F=ma, but that still didn't make much sense. If I could get a nudge in the right direction, that would be awesome.

I know the answer is 6.8 m/s, but I do not know how to go about solving for that.
 
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Hi tangibleLime! :smile:

Use work done = ∫ (force).(distance), and the work-energy theorem. :wink:
 

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