Title: Part IA
Tags: Forces

Q: Proposition. How to solve for the position of a particle in one dimension when we have the potential.
A: \(E = \frac{1}{2}m\dot{x}^2 + V(x) \implies \frac{dx}{dt} = \pm \sqrt{\frac{2}{m}(E - V(x))}\)
Then we can solve the first order equation to get \[t - t_0 = \pm \int_{x_0}^x \frac{dx'}{\sqrt{\frac{2}{m}(E - V(x'))}}\]