How to Increase Velocity of a Servo motor, relative to resistance?
You could interpret this as feedback loop control problem. Say you have a sensor that can give you the speed of the car (e.g. an encoder on the wheels axis). Using control theory and a PI compensator, you can stabilize the RC car speed to a given, constant, value. A block representation of what you are trying to achieve is given below.



The gist of the PI controller is that it drives the error signal to zero for any constant or step-wise constant reference. To implement a PI controller circuit, all you need to do is achieve, with op-amps, the following transfer function.

$$ PI(s) = K_p + \frac{K_i}{s} $$

Where Kp and Ki are adjustable gains. If you have very broad constraints (e.g. current consumption or time which takes for the speed to stabilize don't have to be optimized), these gains can be adjusted purely through experimentation, without much need for control systems theory. If you wish for an optimized solution, then you are in for some studying. Wikipedia link on PID controllers.