We can see that we are limited by the material of the tires and trucks (captured by the coefficient of friction) and the gravitational field (i.e. which planet we are on). Notice that the masses cancel out. No problem if you have a larger vehicle. Yes, there will be more friction, but it will also be harder to accelerate.
constant friction model
Constant power doesn’t work, so what about constant acceleration due to friction between the tires and the road? Suppose the coefficient of friction is 0.7 (a reasonable value for dry roads). In that case, you would get the following plot of speed versus time for 400 meters.
I have included constant power curves just for comparison. This friction model shows that the car continues to speed up forever with the same acceleration. That doesn’t seem right either.
Better acceleration model
How about this? The speed of the car increases, but the rate of increase (acceleration) is lower in the two models. Therefore, acceleration at the start of a run is limited by the friction between the tires and the road surface. And if the acceleration using the constant power model is low, you can use that method.
Before testing this, we need real data for comparison. I don’t own a Porsche 911, so I’ll use this MotorTrend data. 911 and Tesla Cybertruck race. Below is a plot of the Porsche’s actual position on the quarter-mile track and the combo power friction model. (This is the distance on the vertical axis; 1/4 mile is just about 400 meters.)
