Question

A conservative force on a particle moving along the x axis is given by F = (3x2 - 2x)i Which of the following is a potential that is associated with this force?

a. (6x - 2)
b. (-6x + 2)
c. x²-x²+3
d. -x²+x²+3
e. No answer given above is correct.

Answer 1

The potential energy associated with the force F = (3x² - 2x)i is represented by the expression x³ - x², making option c correct.

Step-by-step explanation:

The conservative force on a particle moving along the x axis is given by F = (3x² - 2x)i. To find the potential energy that is associated with this force, we need to integrate the force function with respect to x because potential energy (U) is related to force (F) by F = -dU/dx. Integrating the force function we get:

∫ (3x² - 2x) dx = x³ - x²+ C

Where C represents the constant of integration. Looking at the given options, the one that matches this result after dropping the constant term (assuming potential energy is zero at x = 0, making C = 0) is option c: x³ - x².