I have been recently playing around with some figures in an attempt to find a velocity versus time graph under ideal conditions including air resistance and rolling resistance for a car that I am in the process of fixing. What better incentive to get it running than knowing (at least a rough estimate) of how fast it will be? However, I have run into some problems. I have Approximated a Power versus velocity graph based on a graph that I got from finding a cubic regression from a dynamometer chart of the engine in the car. I then altered tha graph so that instead of having power versus rpm of the flywheel to power versus velocity given the gear ratios and radius of the tire. v=(2pi*x/60)/(Ratio of gear * Ratio of Differential)*Radius of Tire where v is velocity and x is the RPM of the engine. Once this has been found, I determined that the derivative of P(v) would equal F(v) due to the engine. I also looked up the formula for F(v) of air resistance to be (1/2)*Coefficient of drag*Frontal area*Air density*velocity^2. Rolling resistance's would be Coefficient of rolling friction*Normal. From this I get a differential equation that m(dv/dt)=Fengine(v)-Fair(v)-Ffriction(v). However, upon solving this, I get a result that does not make sense at all. Could someone verify that I am doing this correctly, and if not, give me some instructions on how to do this the correct way? Any and all help is appreciated.