I am trying to model a speedometer and tachometer for a simple software model of a car dashboard. I want this to be relatively simple, so for my purposes I won't likely simulate variables such as drag (or, assume that drag is a constant). But I would like to know the general formulas for:

1) Calculating the RPM, depending on a position of a graphical slider representing the accelerator.

2) Using this information to find the instantaneous speed (or, magnitude of instantaneous velocity?).

I am not sure, in the case of 2), what other independent variables I need to consider. Do I need to consider the frequency of rotation of the wheels (assuming a fixed radius), in addition to the RPM?

If anyone can give me a rough explanation plus relevant formulas, or alternatively direct me to other trusted resources online (I have had a hard time sifting through info and determining the accuracy), it would be much appreciated.