f = ma
applies when the force f varies, constant, zero, ...
When a constant force is applied to a particle, this produces a constant acceleration f/m. Then all the usual suvat equations apply. So vertical motion with only a (constant) gravitational force would produce a constant acceleration scenario.
When the force varies (with time), you have to use calculus (integration) to solve for the velocity and position as
acceleration = dv/dt = d^2 x/dt^2
So integrate f/m once to get the velocity, v, and twice to get the displacement x, This reduces to suvat equations when f is constant. If you also included a velocity (time) dependent drag into the previous vertical motion scenario, then acceleration would not be constant and you'd have to use calculus to solve the problem.
When f is zero, Newton 1 (inertia) applies and the current motion is unchanged. This is Newton 2 with f=a=0.