Not sure if the question is sophisticated enough to be posted here, but here goes... I am trying to work out the velocity-time relationship for a vehicle under certain conditions. The 'certain conditions' are: 1. deceleration due to aerodynamic drag and rolling friction 2. acceleration due to an engine less drag and friction now, i will address the deceleration first. I tried to do model this in two ways: a) Equilibrium of forces giving: -D - f = ma (where D=drag, f=friction). putting in the known values, i get the value of acceleration in terms of velocity as: a = -0.00075v2-0.2943 i know that a=dv/dt, so re-arranging, i get: dt=dv/a as a=f(v) Integrating this, i got: v = 19.8 x tan (((t1-t)/67.3) - tan-1(v/19.8)) now, QUESTION: does this formulation make sense? and second, would the angle be in radians or degrees? i put in values both in degrees and radians, but found the deceleration to be quite fast with radians and very slow with degrees. By fast and slow, i mean not in sync with practice. For example: with radians, the vehicle goes from 10 m/s to 5m/s in 15s with a fairly constant gradient. Does it make sense? b) with the basic conservation of energy equation, starting from: KE1 - (Pf + PD)xt = KE2 Putting the values in, i got this relationship b/w time-velocity: t = 666.7 x (100 - v2)/(v x (v2+392.4)) the deceleration (v-t) curve i got was more moderate, with a markedly decreasing gradient QUESTION: How do these two methods compare? What am i doing wrong? What else should i be doing?