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

[tangibleLime]

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 $$x = 0\:{\rm{ m}}$$.

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.

 

[tiny-tim]

Hi tangibleLime!

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