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So the question becomes what speed is the runway moving for the plane to move at all?

That sort of depends on how rapidly the control system for the belt, reacts to the speed of the plane's wheels. Certainly once the plane starts moving forwards, the belt will find itself permanently behind the wheels' speed, and will accelerate to its maximum speed as fast as its control system allows.

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Would it not become infinity? At that point, wouln't the wheel bearings be melted or frozen?

OK, so the belt is allowed to go infinitely fast but the wheel bearings aren't allowed to be frictionless?

If the belt is perfectly frictionless and massless but the wheels aren't, then the wheels will burn out and the plane won't fly. If, on the other hand, the wheels are frictionless but the belt isn't, the plane will fly. If neither belt nor wheels is idealised -- if both are real-world objects -- then the answer depends on whether or not the wheels can survive the belt's maximum speed, i.e. on the engineering of the belt and the wheels.

I agree with JeffS, though, that this is probably not the physics question that the originator was trying to ask.

Peter