Are you high?

The car uses ZERO power at launch. A big fat ZERO. Not 600kW. ZERO. Omega is ZERO.

I am not high, and I did not at any point suggest that the car will use 600 kW at launch. It will deliver zero useful power at zero speed (but consume many kilowatts anyway due to electrical and motor losses), and what I mentioned was

"the assumption that the car is close to using 600 kW for the entire duration of the run; it's lower at the beginning, then reaches the motor maximum at some point when the speed multiplied by torque reaches that value, and stays there."

That's ideally zero at zero speed, rising linearly to the maximum power point. Since the time spent at less than full power is a smal part of the run, a rough approximation of full power for the whole time isn't bad as a starting point.

Using "omega" for speed is just silly. That's the name of symbol used for angular velocity, not the name of a physical quantity. You're not convincing anyone that you have deep technical knowledge with nonsense jargon.

The power use rises linearly, assuming constant acceleration (force before the tires break traction) as torque remains CONSTANT, until maximum power is reached...

I guess what I wrote got across, because that's what I said.

The max speed of the car will be determined by its power/horsepower and that will be where the loads on the car equal the force at the [tires]...

Yes, which has nothing to do with the 1/4 mile acceleration run, which does not reach the car's top speed. The power available at high speed does limit the car's top speed; it also limits acceleration.

Duncan was correct in trying to determine Joules needed. Your 600kW number for the entire run is nonsense unless there's a CVT, which there isn't in a Tesla.

As I explained, the rough approximation of 600 kW for ten seconds is roughly comparable to results of Duncan's approach. No, there is no continuously variable transmission (CVT) but for much of the speed range of a Tesla the power is limited to a roughly constant value, as with almost any EV. That means with increasing speed the torque available decreases, just like a constant speed engine working through a CVT.

And if you do assume constant acceleration , for the 1/4 mile, the POWER used per time curve is a straight line, starting at zero power, and ending, at the quarter mile time, at 600kW. The area under that curve is the energy needed in Joules.

Yes, that's the basis of your 1/2*(peak power)*time calculation, and I agreed with that.

... you gotta deliver the current that makes the torque that makes the acceleration and the voltage that makes the speed, and the max power.

Obviously. You need to deliver the current the motor needs, the voltage the motor needs for that current to flow, and the electrical power that corresponds to those at every point during the run. When the power limit (imposed by the motor controller to protect the inverter and the battery) is reached, power becomes the limiting factor in acceleration. that's true for most of the 1/4 mile run.