If you had a rocket with unlimited fuel and it was continuously firing, would the rocket keep accelerating to a faster and faster speed, or is there a speed limit where acceleration stops
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5$\begingroup$ Theoretically you'll keep accelerating to a greater percentage of the speed of light, but never reach it (it's a mathematical asymptote for anything with mass) $\endgroup$ – Sarah Bailey Feb 2 '18 at 13:18
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$\begingroup$ Unfortunately a rocket with unlimited fuel could never lift up from launch pad on Earth, unlimited thrust and unlimited tank volume would be necessary. If assembeled in orbit, an unlimited number of transfer flights from ground would be necessary to deliver unlimited fuel. $\endgroup$ – Uwe Feb 2 '18 at 16:34
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$\begingroup$ Duplicate of physics SE question here physics.stackexchange.com/questions/100730/… $\endgroup$ – bendl Feb 2 '18 at 17:04
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$\begingroup$ math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html $\endgroup$ – user7073 Feb 5 '18 at 18:38
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would the rocket keep accelerating to a faster and faster speed, or is there a speed limit where acceleration stops
The rocket would keep accelerating and would get ever closer to the speed of light in vacuum. It will not reach that in finite time though. It would never actually stop accelerating, though speed gain would slow down.
