We discuss strategies for the general solution of single-step 1D constant acceleration problems. In a slightly restricted form, these problems have five variables (?"x," "v[subscript 0]," "v," "a" and "t") and two independent equations, so three variables must be given to solve for the other two, giving 10 cases. Instead of the haphazard solution of individual problems, we advocate teaching a strategy for tackling the entire class of problems. We enumerate the possible strategies, and present in detail one which reveals a number of interesting special cases and also allows the possibility of developing an automatic problem generator and solver.