You can see that this is constrained by the materials the tires and tracks are made of (captured by the coefficient of friction) and the gravitational field (so what planet you are on). Notice that the mass has disappeared. It doesn’t matter if you have a more massive vehicle. Yes, there is more friction, but it is 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 assume the coefficient of friction is 0.7 (reasonable for a parched road). In this case, we would get the following speed vs. time graph for a quarter-mile run.
For comparison, I included a constant power curve. You can see that in this friction model, the car will simply escalate its speed indefinitely under the same acceleration. This doesn’t seem right either.
Better acceleration model
How about this? The car increases in speed, but the rate of escalate (acceleration) is slower in both models. So, at the beginning of driving, acceleration is constrained by the friction between the tires and the road. Then, when the acceleration in the constant power model is smaller, we can exploit this method.
Before we test this, we need real data to compare. Since I don’t own a Porsche 911, I’m going to exploit data from this MotorTrend a race between the 911 and the Tesla Cybertruck. Here’s a graph of the Porsche’s actual position on the quarter-mile track with the power-friction wagon model. (This is now the distance on the vertical axis – a quarter mile is only about 400 meters.)