Okay, when you solve for the Force of something, you're solving for it at a specific moment... you're not solving an average. So, when you solve F=(ma)d/dt you will pull m out as a constant, giving you F=m((a)d/dt). You're talking about including the change of mass in a scenario... If that's what you were looking for, then the Force (F) would be notated with an integral before the F AND m would have to be changed to (dm) to represent (dm/dt) (change of mass over time).
tldr; Amamin is right.
source: high school physics and 10 years as a mechanical engineer.
