A portal is as another commenter has framed it, essentially a hula hoop with a different space on the other side of it.
It doesn't matter how fast a hula hoop falls over your body. You are not going to be launched out of the other side of the hula hoop even if the hula hoop is moving at the speed of light.
If the hula hoop is moving at the speed of light you are more likely to be killed by the shockwave of all of the atoms in front of the hula hoop compressing to adapt to the sudden intrusion of a lightspeed object with Mass, in which case it is very likely that you would pop out of the other side as some sort of soup, but that would not be because of your interaction with the portal inside of the hula hoop, or the acceleration of the hula hoop itself but rather the acceleration of the things around the hula hoop as it moved through space.