This might not be the right formula.
Now we have an accurate assumption!
A better relation would be y(t)=-s(t) from the original problem state where the magic conveyor matches the speed of the wheels In the opposite direction
Takeoff velocity is 72 m/s? Sure why not. Then the magic conveyor will be going -72
m/s....None of this Mach 10 or speed of light blather.
The wheels will always be spinning at the same speed as the conveyor belt.
If the conveyor belt is moving at 100 mph and the wheels of the plane aren't turning, wouldn't the airplane have to also be moving at 100 mph? If 100 mph is fast enough for the plane to take off, won't it take off?
(Hint, the speed of the wheels and the speed of the conveyor belt are irrelevant. It's only plane's speed relative to the air that matters.)
Yes! I think a major confusion for people is that a wheel turns at revolutions/time and things move at distance/time.
By wheel "speed", you have to take the speed of the hub because that's the only point that moves forward on a fixed horizontal vector. ALL other points on the wheel are spinning and have different velocities based on their angular position and velocity. Get that in your head and just divide the difference in velocity between ground and hub by the radius and you have the angular velocity
I'll post my free-body diagram again just because it reminds me of simpler times.
The increased wheel rotation will make the plane work harder, but I can't imagine it imparting enough rolling resistance to override the engines.