Technically, relative to the ground the object becomes moving infinitely fast as soon as it enters the portal. I think a more intuitive answer can be found by replacing a nice discrete object like a box or group of people with a long pole that enters the portal lengthwise. Obviously, it's going to have to be exiting the other portal at whatever speed the first portal is moving. The out speed should always be the same as the relative speed of the object to the entrance portal, it's the only thing that makes sense, and also the only way to appease conservation of momentum.