Originally posted by: DrPizza
As you're dealing with rates, college algebra is inadequate. As even Kyle will admit that there are different values for the acceleration (the acceleration wasn't g the entire time; only a portion of the time), then you're dealing with jerk. (The time rate of change of acceleration, aka d3s/dt3 or d2v/dt2 or da/dt) As Kyle is using a formula/algebra based physics set of equations, it's doubtful that the physics book of whoever it was that Kyle copied and pasted his "math" from even mentions jerk. Nonetheless, Calc II & differential equations at the very least.
A little more on jerk here; nothing too technical:
http://en.wikipedia.org/wiki/Jerk_(physics)
But, as soon as you say that the acceleration of the building is changing, then you need some deeper math to explain it. (edit: conceptually, it can be explained why the rate of acceleration changes. However, since Kyle has some specific numbers, then we need the math to verify that those numbers either are or aren't possible.)
Also, not mentioned yet is how the amount of force (or resistance as Kyle calls it) provided by a material changes depending on the rate at which the force is varied to its maximum force.