understanding physics 01: derivation of fundamental linear motion equations

i'm tutoring someone in physics again and i was thinking about how to explain why conservation of energy is so fundamental in physics but specifically in classical mechanics while driving to work this morning. one of the reasons i love physics more than other sciences is that it conceptual understanding doesn't require excessive blind memorization of symbols, constants, tables, taxonomic ranks, etc. If you can remember Newton's laws, understand that energy is conserved, know how work relates to force, distance and direction, you pretty much just need two equations and basic calculus to solve any problem through intermediate mechanics: F=ma and v=dx/dt. there are numerous equations you could memorize to solve problems involving linear and angular motion, but all of them are derived from v=dx/dt (i guess you also need to know that there are 2pi radians in a circle for angular motion problems). i remember that at the start of every exam, i would derive the equations for distance, velocity, acceleration and time and, for whatever reason, this would always calm me down. i've decided to see if i can still do it and will post my notes when i finish or give up