I looked over various links cited above, and the F = m*a =m*dV/dt is a simplification to get reasonable answers.
Many years ago I wrote a trajectory analysis code in fortran that employs similar equations that Open Rocket uses. Clearly Open Rocket is an ideal Model Rocketry design tool with its visual and ease of inputting components and calculating results. So when I came across Open Rocket two years ago, and read its documentation, I started using it.
Recently I decided to compare the results of Open Rocket with my Trajectory analysis code, and I always found that my maximum velocity and drag were higher than Open Rocket. So after thoroughly investigating the thrust curves, the 1976 US Standard Atmosphere, the drag calculation procedure, and the numerical integration scheme I am using, I was baffled that even though all the parts were producing similar results (even about the same Cd) the overall answer was different.
So I decided to omit the m*dV/dt part of the equation. Once I did that, my results and Open Rocket results came in to close agreement (still slight differences in Cd and therefore V(t) and h(t)).
So I now have two options in my old Fortran Trajectory code:
First, what I have been using d(m*V)/dt
Vip = [ mi * vi + sum of Forces( Thrust, Gravity & Drag ) * delta time ] / mip
and
Second, what Open Rocket uses, m*dV/dt, omitting the V*dm/dt term
Vip = vi + sum of Forces( Thrust, Gravity & Drag ) * delta time ] * 2 / ( mip + mi )
As I see it, the second option is a simplification, that will produce reasonable results, but the first option should be the more accurate analysis.
If I am wrong it would be helpful for me to understand why.