Question

You may also have a single acceleration for a system of multiple objects (think of a train all objects move at one speed and acceleration, but each car has its own mass)

In this case would FN = (m1 + m2 + m3 + m4 + ... + mn)a a valid way of writing this sum? Why or why not?

Answer 1

If a train pulls all its cars behind it, the force required to give them acceleration $a$ will depend on the sum of masses of all cars. To accelerate a car $i$ to acceleration $a$, force $F_i$ is required:

$$F_i=m_ia.$$

Many cars with other masses will require a corresponding force, which will result in the equation shown in the condition of the problem.