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>How extended is an extended mass? For something bigger than a two
atom molecule, I assert that an f(t) applied to it and the a(t)
are NOT symmetrical. They are not coincidental in time nor shape.
In other words, the idea that f = ma is OK for non-experts and
teachers, to paraphrase another contributor ...but only
represents a first order relation.
This has been further expanded at this point in the thread, but my
take is still that f(t)=ma(t) precisely, even for extended systems. I
don't think anyone would consider the spirit of this discussion to be
generally true if f(t) is at one place and a(t) is at another.
In an extended mass system (connected by springs, for example),
applying a force at one end, and considering how it propagates, and
the concomitant phase shifts in v and a down the line, is I think, a
different issue. But f(t) is still ma(t) precisely (no causal time
delay) for any of the individual masses.