This question was asked at SE and was eluded with arrogance. I joined this site of TP to see if it can be adequately discussed, even if it may appear 'weird' to a superficial reading.

$F=m*a$ is Euler's first law of motion. It is wrongly identified with Newton's second law, since we know for sure he had seen the original proposal by Hermann in **Phoronomia** and refused to accept it because it was not his idea of **vis motrix**. In particular, if the concept of force is tied to $a$, it cannot be geometrically represented.

The formula is indifferently used as an

- **a priori** definition, as in the case of gravity, where $g$ is **not** a force but a *rate* of uniform, constant and unlimited acceleration $a=10m/s^2$: any mass, no matter how large, will get same *a* and the force can follow the mass any length: therefore the effect (RHS) is equal to the cause (LHS) : $F_g = m*g => m*10m/s^2$ and when we know time: (s = 5) we can determine the increase of velocity (50) and the impulse the body acquires: $J=m*50m/s$ and if we know the value of mass and of $v_0$ we can determine the increase in Ke.

- **a posteriori** definition, in 99% of instances in real life, when not a force *at distance*, but a concrete push/pull is involved, when not a rate but an ordinary force expressed in newtons is involved. Consider a steel spring (k=200, d =.5) which when fully compressed can exert a force of 100 N and body B (m ) , and B' (2m). The question is:

- " ..given the force, the time it is exerted $J=F*t=100*0.25$ (and , in this case, the distance d, to boot) can you determine the effective velocity acquired by B/B' if you do not know their mass, and consequently the change of momentum J"? If you can't, can you at least affirm that, according to the formula : $a=F/m$, $v_B = 2 v_{B'}$

- "...even if you know the value of mass, can you determine the increase of v,p or Ke?

Before you downvote or post a negative comment, ask yourself if you understand how complex the question is, and if you can answer such an apparently simple or weird question.

If you cannot answer it, do not sweep it aside.