v is in m/s, and t is in s. That's where the m/s2 comes from.
As for the encumbrance, I'm saying I don't think that's how it works. It does say 'push' the rod ten feet, not drag. Plus, I believe you can only drag at 5 feet per round. Plus, I'm fairly sure that that is not how the rod would work in such a situation. It doesn't weigh 8000 lbs.; it can just support 8000 lbs.. There are plenty of things that can support a weight but weigh less than it. And for just as many, the opposite is true. It remains in one place, and regardless of how much you pull on it, you will not budge it without making the strength check.
As for your second note, I must disagree. As soon as you took the rod with you, from falling(theoretically being wrenched upwards and thusly decellerating from the sudden jerk before continuing on your gravity assisted journey), the net force acting on the rod relative to you would be 0, discounting waving it back and forth. Of course, should you activate it or whatnot, you would still be moving, and possibly place 8000+ pounds of force on it again, breaking the magic, but this should still slow you down. If you pressed/activated it quickly enough in succession, you might be able to slow yourself down enough to come relatively safely to a stop. Besides all of this lies the matter that it would only fail as soon as all of your weight was forced to be supported by the rod, rather than continuing in freefall, and depending on how one gripped the rod(and somehow managed to keep their grip, as I suspect that it would be more likely for you to let go and keep falling than break the rod's magic), you might be able to have slowed yourself or spread out the direction of force so that it would not break the rod's magic.
However, I must also disagree with you about the harness of your body 'striking' the harness of your armor. You will be touching your armor. It is simply about the rate of decelleration, at least in reality, that and the area in which the force caused by the decelleration is spread out. Sure, if you had on a breastplate, poorly made, simple, or otherwise just a few pieces of armor essentially hanging on you, that would be the case. But if you were wearing full plate or half plate, or even chaimail? The straps distribute the weight over your body, thusly also distributing the force. With chainmail. You would likely come to hang around the rod, as the chains are more elastic as a whole than plate. It would also affect the entire region in which chain was able to touch you. Of course, more likely, the chains would simply snap and you would keep falling, depending on your speed.
This also brings up the question of how they interact with holding up weights together, and whether, should they be round, if they can roll in place. One might be able to make a conveyor belt with them over many miles of distance, descending only slightly in a similar fashion to Roman aqueducts, using any of a variety of materials to form a perfectly straight plane, most likely through magic, across the top of them, or simply letting long objects roll down them. Similarly, if one has 3 equally distant immovable rods, forming a triangle, and places a weight with a center of mass directly above said triangle of a mass of 20,000 pounds, would they fail? Would it be distributed and none of them fail? Would all of them fail from having a weight of 8000+ pounds placed upon them, supporting only part of it or not? If the triangle they formed was at an angle, or the weight was focused on one or two rods more than the other(s), what would happen? Would the one fail, and the others, possibly weighted down by the mass momentarily at it's full weight, fail also? Would two fail, having each to support more than 8000+, but the other remain, having had only to support some lesser number?
Although, I must also question my own proposal of them retaining the same velocity, acceleration, or jerk, for, presumably, if you were to activate it whilst falling, it should keep falling with you were you to do that, which it almost certainly does not.
I feel like an actual mage debating with fellow mages about magical interactions as compare to physics. :3