Answer
The particle has zero speed at X=6m.
Work Step by Step
The particle begins at rest. For the first 3 meters it is pushed in the positive direction at varying magnitudes of force. From X=3 to X=6, the particle is pulled by the same magnitude forces, in the negative direction. At X=6, the particle has been pulled in the positive direction and the negative direction with the same amount of force. The total forces are equal and opposite so they cancel each other out, effectively stopping the motion of the particle for an instant.
