understanding physics 01: derivation of fundamental linear motion equations (cont'd)

i finally got around to doing some of the work this morning (note: since i don't know how to insert the integral symbol, i'll use an ampersand instead):

• v = dx/dt, vdt = dx, &vdt = &dx -> vt = x (assuming x0 is zero, v is avg velocity)
• a = dv/dt, adt = dv, &adt = &dv -> at + v0 = v
• distance (w/o vf): x2 - x1 = v2t - v1t, v2t = (1/2)at^2 -> x2 = x1 -v1t + (1/2)at^2
• velocity (w/o t): x = vt, v = [(v + v1)/2], t = (v - v0)/a -> x = [(v + v0)/2][(v - v0)/a] = [v^2 - (v)(v0) + (v)(v0) - v0^2]/2a = (v^2 - v0^2)/2a, 2ax = v^2 - v0^2, v^2 = v0^2 + 2ax