When we say "something accelerates" what we mean is "its velocity increases over time". Its acceleration could also increase over time, but that is not a requirement. When you ask "what is the acceleration limit" it seems like you are not clear on that fact. The velocity of the rocket relative to the Sun could be increasing for the first half of the journey, while its acceleration (or deceleration, on the second half) could remain constant. At 9.8 m/s² the crew would cruise at a comfortable 1G.
But let's consider that the acceleration increases over time. The maximum number of Gs the human body can withstand has been studied in astronauts and fighter pilots. They can withstand 8 or 9 Gs for some time with special training and compressive clothing. That puts the biggest acceleration at about 99.8 = 88 m/s², but this would have to be done in bursts, with special clothing and training. The maximum acceleration for being able to perform regular human tasks like walking or taking readings would be much less however. I don't have figures for that, but I think the risk of accidental bone fracture increases dramatically when we go above our specs. 2Gs would already be too much.
All these questions are kind of moot for now because with the fuels we currently have we can only sustain acceleration for a very limited amount of time.
I also want to point out that the fastest point from A to B in space must* take into account that space is not always empty. A third object C can be used to give a "gravitational assist" to a spacecraft. Or its influence might have to be counteracted by spending extra fuel (making an alternative to the straight line between A and B preferable).
What I meant was "what sustained acceleration could humans tolerate? Others have answered that question, and also provided the surprising (to me, at least) bit of data that a 1G constant acceleration -- currently not remotely possible -- would put the entire solar system within easy reach.
And yes, I understand about gravity assists and the like.
But let's consider that the acceleration increases over time. The maximum number of Gs the human body can withstand has been studied in astronauts and fighter pilots. They can withstand 8 or 9 Gs for some time with special training and compressive clothing. That puts the biggest acceleration at about 99.8 = 88 m/s², but this would have to be done in bursts, with special clothing and training. The maximum acceleration for being able to perform regular human tasks like walking or taking readings would be much less however. I don't have figures for that, but I think the risk of accidental bone fracture increases dramatically when we go above our specs. 2Gs would already be too much.
All these questions are kind of moot for now because with the fuels we currently have we can only sustain acceleration for a very limited amount of time.
I also want to point out that the fastest point from A to B in space must* take into account that space is not always empty. A third object C can be used to give a "gravitational assist" to a spacecraft. Or its influence might have to be counteracted by spending extra fuel (making an alternative to the straight line between A and B preferable).