I am literally 5 compared physicists-a tire rolls down hill and it keeps rolling faster can it increase in speed infinitely as long as the hill is infinitely large?
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This is an interesting problem because it forces us to examine our assumptions.
We have two possible interpretations of the infinitely long hill, for example – is gravity constant or not? (I suppose you could even argue for a 3rd where the hill itself had mass so as you went down the direction of gravity would change).
Connected to that we have the vexed question of air resistance – do we assume none, a constant air pressure or does air pressure increase as we descend the hill?
We know that there is friction between the tyre and the ground, because the tyre is stated to be rolling (rather than sliding) and the rate of roll is increasing.
My answer would be that the tyre would increase in speed until air resistance balanced out the forces. Remove air resistance, and there is a race between the tyre flinging itself apart from centrifugal forces and something odd happening at the interface where rubber meets ground, causing the tyre to stop accelerating the spin and move to a constant spin speed but sliding across the ground too, so the speed of the tyre doesn’t match the speed across the ground. This would also cause the tyre to disintegrate quickly. Assuming though that you can make the tyre indestructible in some way, what you have is essentially a magic gravity powered particle accelerator. I’m pretty sure that there would be some gotcha that makes the tyre subject to the normal issues with approaching lightspeed (steadily increasing mass means the acceleration reduces so you asymptotically approach lightspeed), but my currently horribly sleep deprived brain is refusing to come up with a reason that makes sense in a magic universal gravity field, as the mass of the accelerated object cancels in those equations. In the most extreme case, where something in the magic allows that continuous acceleration at a constant rate, the mass of the tyre would quickly increase to the point where it became a black hole itself, taking us into exotic physics country where you’d have to work out how the magic gravity field interacted with the singularity. *Something* must stop it accelerating at a constant rate or it’ll quickly become an object with a mass-energy high enough that we have no reference outside the big bang itself.
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