You can see that it is limited by the materials in the tires and track (captured by the coefficient of friction) and by the gravitational field (so what planet you are on). Note that the mass has canceled out. It doesn’t matter if you have a more massive vehicle. Yes, you get more friction, but it’s also harder to accelerate.
Constant friction model
Since constant power doesn’t work, what about constant acceleration due to friction between the tires and the road? Let’s say the coefficient of friction is 0.7 (reasonable for a dry road). In this case, we would get the following plot of speed versus time for the quarter mile run.
I included the constant power curve just for comparison. You can see that with this friction model, the car will continue to increase its speed forever with the same acceleration. That doesn’t seem right either.
A better acceleration model
And this? The car increases in speed, but the rate of increase (acceleration) is the lower of the two models. Thus, at the start of driving, acceleration is limited by the friction between the tires and the road. Then, when the speedup using the constant power model is lower, we can use this method.
Before testing this, we need real data for comparison. Since I don’t own a Porsche 911, I’ll use the data from this MotorTrend race between a 911 and a Tesla Cybertruck. Here’s a plot of the Porsche’s actual position on the quarter-mile track with the power-friction combo model. (This is now the distance on the vertical axis: a quarter of a mile is about 400 meters.)