Actually, f=ma has little do do with it, other than determining 'a' as the force does not change(charge weight stays the same). The spike in pressure is cause by the increased time the projectile stays in the barrel. This increases the peak pressure as more powder is converted to gas (ie more pressure) before the projectile moves enough for the peak pressure to drop away. Much the same as a pressurised water system.
The Big determining factors on this increase in barrel time are going to be mass or force (pill size & charge), static friction (friction build up before the prjectile moves) and of course barrel friction (givin that the projectile is slighly over bore). This is why they say do not use reloading data from 1 120 grain projectile to the next, as the frictional forces have a significant effect on initial pressure, veloctiy, and peak pressure achieved in the chamber and barrel. (as does projectile weight and charge size)
Again, no expert on ballistics, just observations based on what I remember from my engineering days
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