Like compound interest, constant acceleration is powerful. 10/m/s/s gets you to 30,000 m/s in 3,000s. That's .1c in less than an hour. The energy required is mv^2, m being the mass of your vehicle, and you can annihilate anti-matter to get, theoretically, Mc^2 of energy out of it. That means you can get to .1c with M=mv^2/c^2=.1^2 or 1% of your vehicle mass of anti-matter. That's a small enough number to leave a lot of wiggle room.
(Much smaller, and more realistic, accelerations are possible over longer periods of time, but require using the use of relativistic equations of motion.)
I think you mixed up m/s and km/s. The speed of light is 300,000,000 m/s, so 30,000 m/s is only .0001c. At 1g, it actually takes a month to reach .1c. (Still, your point stands.)
(Much smaller, and more realistic, accelerations are possible over longer periods of time, but require using the use of relativistic equations of motion.)