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Hmm. The problem with statement #1 is that unless we change the gearbox, acceleration at a defined speed will stay the same, since peak acceleration will always be done in the lowest gear possible.
I would say your analysis of statement #1 is correct, however I'd like to add to the statement that it is conditional on how much traction is available. You are also correct that friction plays a role, but as speeds increase, drag becomes exponentially greater, and therefore a real factor as speeds climb.
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