When attempting a solution to a problem on variable motion, it is important to represent velocity and/or acceleration in a way that leads to a differential equation that can be solved, i.e. not more than two variables appear in that equation. A summary of suitable differential equations for most situations given below.

When a is a function of displacement, f(s), use:

When v is a function of displacement, f(s), use:

Remember that these relationships apply when a, v and s(or r) are given in cartesian vector form.