> F = engine_torque * wheel_radius * slip_ratio

This one can't be right. Force would be relative to rear wheel torque
divided by tire radius.


> I didn't know what would the slip
> ratio be if the velocity is 0.0 (Starting up).

You need a different formula. Some formulas treat a tire as if it
were a spring.

Note that these are "idealized" formulas to make modeling a car simpler.
The actual real world formulas for a tire are more complex.

> Also what value does the traction coefficient usually have?

For a peformance tire, around 1.0. For a road racing slick, 1.5 or
more. For a drag racing slick, over 4.0. You can't make tires out of
table tennis rubber (way too soft), but it has a coefficient around
7 or 8.


> So how can I solve this problem?

As mentioned, treat the tire as a spring.

> As a side question, is there any other torque (that I need to worry
> about) exerted on the wheel besides traction, engine and brakes?

Traction just puts a limit of the torque. The engine/gearing, and
brakes generate a torque. If the car is on an incline, then gravity
applies a force to the car and tires.