Final answer:
The work done by the force is -16 Joules.
Step-by-step explanation:
A conservative force is one for which work done by or against it depends only on the starting and ending points of a motion and not on the path taken. In this case, the force given by F(x) = (3x² - 2x) N is a conservative force. To find the work done by this force as the particle moves from x = 1 to x = 3, we can use the work-energy theorem.
The work done by a conservative force can be calculated by taking the negative integral of the force with respect to the displacement. So, the work done by this force is:
W = -∫(3x² - 2x) dx
W = -[x³ - x²] from 1 to 3
W = -(3³ - 3² - 1³ + 1²)
W = -16 J
The work done by this force as the particle moves from x = 1 to x = 3 is -16 J.