but the thing I was wondering the article says it's moving at 1.5 million miles an hour,so when it does break free from the black hole will it continue to accelerate or slow down.
well if there were no other influences, it would continue at the velocity it was traveling at when it escaped the gravitational field of the black hole
*. however, since it's going to be passing other bodies, it's going to change both speed and direction, as each object it nears will begin by pulling it (thereby accelerating it), and as the star passes the object, it will begin to get pulled towards the object (altering trajectory again), and as the star pulls away from the object, the object's pull will decelerate the star. i think overall the star will be decelerated, as it will inevitably collide with other things in space, thus transferring it's kinetic energy to the object it collided with - even assuming the star absorbs the object, you still have the same amount of energy distributed across a greater mass, so the overall velocity will decrease.
* assuming space as a vaccuum, since there are no objects to provide friction or collide with the star, there's nothing slowing it down. by the same token, there's nothing providing an impulse to speed it up, so theoretically it would stay the same. however, you're talking classical physics vs. newtonian physics ;)