Because Work = Force times Distance = Energy. Acceleration is the result of energy added (by doing work) to a body with inertia (mass). Now if you ask what is inertia: that is the right (IMO unanswered) question!
He addresses that basic science makes this confusing because there's a curvature term that is usually left out of acceleration equations which balances out when you're accelerating along your curvature (e.g. against gravity), instead of along your spatial coordinates.
Ah, of course, you're right. Thanks for pointing that out! I didn't really think about it at the time, but the equation you end up with if you use the acceleration approach results in a v^2, which makes sense when you consider that the equal energy dissipation approach is equivalent.
I'm studying physics right now, I can say I agree with everything you said.
One thing I'd like to expand on to those who don't know how greater energy means greater speed.
The kinetic energy equation is 1/2massvelocity^2=KE
Since the KE increases from the momentum transfer, and mass of the object stays constant, the only thing that can change is velocity, where it has to go up.
ex: KE=2, m=1
2=1/21v^2, v=2
Now if some momentum were transferred, and the kinetic energy increased to KE=8,
8=1/21velocity^2, velocity=4, since the mass can't change
No, it's the acceleration. The forces are absolutely different between your two examples. The energy is the same, but in one case the energy is dissipated over a longer time, requiring less acceleration and thus force. Jerk and acceleration will tend to be correlated in collisions, but you can construct cases with very high jerk and low acceleration which are just fine and cases with very high acceleration and low jerk which are not at all safe, though the latter case will generally require a lot more energy (fighter jets and rockets, for example).
I was shocked at the concept of acceleration for this very reason. I thought there was just velocity up and velocity down because I got my notions of physics from video games.
That is an amazing empirical fact. As a physicist, my mind goes to something like the acceleration of the acceleration (jounce), but I can't find a model for what is being observed.
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