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Similarly, in the gun, there are two ways to increase the barrel time. One is to reduce powder charge, which lengthens barrel time by reducing the force accelerating the bullet, simultaneously reducing recoil. The other is to increase the bullet mass so the exact same increase in barrel time is needed to get it out of the muzzle, but that does not reduce the accelerating force. So now you have the same original force applied for a longer time, accelerating the gun mass more, increasing recoil.
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We aren't disagreeing, but you pointed out this
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When the same pressure is applied to them they accelerate more slowly, subjecting the gun to the same equal and opposite force for a longer time. That accelerates the gun more to the rear.
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was slightly confusing because it sounds like longer barrel time increases acceleration, which it by definition cannot. What you should have written is:
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When the same pressure is applied to a heavier bullet greater inertial and bullet to bore friction resistance causes them to accelerate more slowly, subjecting the gun to the same equal and opposite force for a longer time. This longer time interval allows acceleration to result in a greater final velocity.
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Because even if acceleration is less because of increased barrel time, final velocity can be increased because you have more time to build up velocity.
I like the kid and fat aunt analogy, because both are being accelerated at -9.8m/s/s for 5 seconds. Time of acceleration is immaterial as the acceleration still results in a velocity of zero (providing the chair don't break). But here is another analogy, if two different balls are dropped from 20 feet up, the time it takes for them to hit the ground is exactly the same, the time of drop is exactly the same, but the impact is different, you can see my point that barrel time isn't the deciding factor in impact, but the energy required to get the balls to 20 feet to begin with. It all comes back to energy, not time.
Sorry to argue so intensely over precision, but I hope some folks have found it amusing if not educational.
Jimro