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But there is a specific circumstance that I don't understand it. This is the easiest example I can come up with:

Lets say you are standing on a trampoline. The trampoline will go down a bit from the force of you standing on it (ie, your mass * 9.8)

But, if you start jumping on it, the trampoline will go down further than it did when you were only standing. Logically speaking (well, my logic) it takes a greater force to push the trampoline down further. However, according to F=ma, your force is still your mass * 9.8 (the same as when you were standing)

So it seems to me that force should somehow directly incorporate velocity. I've talked to my physics teacher and he didn't really have an answer, but one thing he did tell me is the equation for momentum, p=mv, so F=p/t, so F=mv/t. But that doesn't help any because the velocity still gets divided by time, so it doesn't really have a direct influence on the force.

I'm guessing there is some concept I just probably haven't learned yet, but this is really bugging me. Any help?