I am puzzling my head around the Veritasium famous video right now: https://www.youtube.com/watch?v=yCsgoLc_fzI
Also the Physics Olympiad problem Part B1 https://www.aapt.org/physicsteam/2019/upload/USAPhO-2013-Solutions.pdf
I fully understand (I hope) the case when the car has a speed v higher than the speed of wind w it will accelerate until it reaches an constant speed where the power transferred from the wheels is bigger than the power of the propeller.
What is puzzling me is the following experiment: Suppose we have a very long treadmill (so we can simulate the case of constant wind). If we were to just place the car in the treadmill without rolling the wheels. The car would go initially backwards with constant speed the one of the belt backwards. It will create some drag with the air of the room which will cause the car to slowly start rolling forward. When it starts rolloing forward the propeller will rotate as well, but the air is still coming from behind the propeller. Is it possible that the car exceeds the one of the belt (assuming the aerodynamic shape of the car does not change)?
Will it start rolling forward with speed v greater than w, for any speed w of the belt?