Relativity’s a funny thing. Not only does time get slower, but length (along the vector of travel) gets shorter and mass gets heavier. This is all from the POV of an outside (i.e. not experiencing acceleration) observer, of course.
Leaving out acceleration time (which is actually pretty negligible for long voyages as long as you have a very, very, very large source of energy… more on that later), you can figure out by what factor time slows, length shortens and mass increases by plugging this formula (the Lorentz Transformation) into Excel:
=1/SQRT(1-(A1/100)^2)
Where A1 contains the percentage of light speed you’re traveling.
Try it and you’ll see the truly dramatic effects come as you pass 99% of lightspeed. At 99%, time is 7 times slower; at 99.9% it’s 22 times slower, at 99.99% it’s 71 times slower, etc. As you keep adding 9’s at the end, the increase gets pretty dramatic… it’s what’s called an asymptotic curve. If the final five wanted to make a 2,000-year voyage (i.e. a voyage of 2,000 light years) in only one year, they’d have to travel 99.9999875% of the speed of light.
The problem in all this is energy. If time’s slowed down 2,000 times, your mass has increased 2,000 times. (You don’t feel heavier, it’s what’s termed “relativistic mass”). That means you need 2,000 times the force for an incremental change in acceleration than you need at rest. So it actually ends up costing you more energy to increase from, say, 99.9% to 99.99% of lightspeed than it cost you to go from 0% to 99.9% of lightspeed, because of your increase in effective mass.
BTW, you experience time dilation in your car as well. If you’re traveling 60 mph, which is 0.015% of lightspeed, time travels 0.000001% slower. It’s kind of hard to perceive, of course…
As for acceleration/deceleration: it takes about 35 days at 1 gravity to get to 90% lightspeed, where relativistic effects are still minimal. After that, diminishing returns sets in: the same force applied gives you decreasing acceleration. But as long as energy isn’t a problem, you can keep accelerating.
Why can’t you every reach lightspeed? Because time would stop for you, you’d be two-dimensional (zero length) and infinite mass. That would be a problem.
(I’m pretty sure I got all these numbers right, but my disclaimer is it’s been 10 years since my university physics classes.)
I just pop-in and out every year or so, like new BSG content.