Artificial Gravity

Why can't a space ship, instead of giving an intense thrust at the beginning of the trip, just continuously accelerate at 9.8m/sec*sec for the first half of the trip and turn around and accelerate at the same rate in the other direction for the other half of the trip (reaching zero velocity at your destination)? In one year, you're already going 1/10 * the speed of light, plenty close to experience the effects of relativity. You also get gravity for free assuming the "floor" of the ship is on the same side as the thrusters.