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... it makes sense to say the following. Bob pushed on the car, as a
result it accelerated. However, "The car accelerated, as a result Bob
pushed on it" does not make sense. Yes, the math does not recognize the
illogicality of the second statement. And yes the push and the
acceleration are simultaneous and the equation does not recognize
causation. However to push Bob had to first move his hand prior to the
acceleration, thus establishing causality.
Causation is a judgement, and not necessarily a mathematical fact.
The real reason for establishing the causation link between forces and
acceleration is ultimately pedagogical. Students who do not establish
this link usually exhibit very fuzzy thinking.
Unfortunately they do not think in terms of math relationships.
...not formal thinkers.
...do not really understand equations with 3 variables.
They must first make a link that acceleration is caused by force, then
they must make the reverse link that when you observe acceleration, you
know there must have been a force. Making one link does not automatically
establish the other.
Do not cause and effect form a temporal sequence.
If cause and effect are simultaneous naming one as
cause and the other as effect does not make sense.
Later on in a very advanced course they might understand that the
mathematical description does not need causation.