Considering the Lennard-Jones potential,
$$V(r)=\frac{A}{r^{12}} − \frac{B}{r^{6}}$$
How does this relate to force or energy? I suspect that there is some physics equation I'm forgetting. I know that $F=−\nabla(V)$, but that's a partial derivative with respect to time, and I don't see how time comes into effect here. Also, the derivative of energy (work) with respect to displacement is force, but I'm not sure how to connect that to potential.
An example application that stimulated this question: given the interaction potential above, how would you find the interaction energy between two systems?