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But force is the mass x the acceleration. That indicates how strong something had to be to accelerate that mass at that rate, but not how hard that mass will impact.

The acceleration doesn't matter at all in an impact, right? A car hitting you at 100 mph does the same amount of damage if it took five minutes to reach that speed as it did if it took several seconds. So, if force is mass x acceleration, it doesn't make sense to measure the impact in terms of force, only what the car had to have in order to accelerate like that.

And then, is impact force an existing term different from the normal term force? What do very descriptive things like pounds per square inch come under? Kinetic energy describes the magnitude of the event, but then these compare the impact to weight over a certain area.