"an equation should be acceptable if the student can derive it."
High school freshman are not very good at deriving. The rearranging of a single equation with 3 variables is a challenge for 1/2 of them (seemingly insurmountable for 1/10 of them).
I plan to try the graphical analysis approach and find the relationships in that manner this semester (don't often teach freshman). I suppose this would count as deriving. I don't know how much success (or time would be required) to derive a relationship from multiple other relationships.
Paul Lulai
Physics Teacher
St Anthony Village S.H.
3303 33rd Ave NE
St Anthony Village, MN 55418