Re: think about this...
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It was assummed and I believe the OP specified a no-slip condition between the wheels and runway. I don't believe that condition can be reconciled with the condition that the wheel's speed = runway speed if the wheel has a tangential acceleration with respect to the runway.
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I just reread the OP, and I didn't see where it said the wheels don't slip. If the wheels can't slip (I'm not positive, but my intuition says this would be the case on perfect bearings too), then the conditions of the problem make no sense. If they can, then the plane takes off.
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