Derivation of Impact Force Formula

They're out there right now. They're in my living room. I don't know how long this will go on, but I think if I left it up to them, it would be all night.
The boys are playing with Legos. There are hundreds of little plastic interlocking blocks spread in a thin layer across the floor. I live in terror of having to walk around tonight in the dark and finding a carelessly overlooked piece or two. That's the worst part.
The best part is watching and listening as they negotiate the design and building of their vehicles. There are turbo engines and spoilers that are wider than the machines are long. There are front wheels that are one quarter the size of the ones on the back. They are all equipped with some kind of tactical weapon: lasers, photon torpedoes, missile launchers. But most of all, they all feature prominent front grills, since the game tonight is seeing just what kind of impact it will take to spray the component parts of at least one of the vehicles over the entire surface of the living room rug.
It's a stress test. The sound of Legos spraying in hundreds of directions at once is followed immediately by the sound of three boys giggling maniacally. This is an interesting development, after spending years prior to this protecting and preserving each Lego creation in its completed, pristine form for months at a time. It's the beginning of a new phase. Nothing lasts forever. Like most things in this life, Legos are transient.
It's getting quiet again now. The discussion has turned to who is the winner of the demolition derby. There is a lot of respect being paid to each of the designers, with suggestions offered to the vanquished. It's time for a chocolate chip cookie break.