Yes, but the real problem is fuel( even with antimatter ). And radiation.

I agree that the real problem is fuel, but 10 years isn't quite long enough if you are going to accelerate halfway and decelerate halfway to arrive at low speed. For a 2,500 light year trip composed of two 1,250 light year legs, the time experienced by the ship will be (in units where c and a are both approximately 1):

2 * T(1250 lyr) = 2 * (c/a) arccosh (ad/c^2 + 1) = 2 * arccosh(1250 + 1) = 2 * 7.8 = 15.6 yr.