> The engine is directly coupled to the wheels.

Assuming the clutch is engaged, yes this is pretty much true, the only tiny 
difference can come from twisting in the driveshafts and bending of the 
teeth on the gears.  So it's pretty much coupled :-)

> Unless the car looses traction, the forward motion of the car and the 
> rotational speed of the wheels and engine all have a simple linear 
> relationship.

Except pretty much the whole time, part of the tyre has lost traction with 
the road, if it hadn't then it would mean there were no forces being 
generated, and you wouldn't go anywhere.

There's a quantity called "slip ratio", which is the ratio between the 
actual speed the wheel is rotating, and what it "should" be (ie vehicle 
speed divided tyre rolling circumference).  The slip ratio (SR) is never 
exactly 1, only when you are applying no forces to the wheel (ie no power 
and no braking).  If you brake moderately hard, it can easily go down to 
0.8, and under normal acceleration can be 1.05 or so depending on your 
tyres.

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