kg/sec can be a sort of flow rate, e.g. a dump truck dumping off stone can be measured in those terms. That's a common example. Multiply this rate by the seconds it took to dump the stone and you have the total weight dropped.
It think too complex at times, as for the kg/sec^2, these are the units for a spring constant (Hooke's Law). Of course such springs are used in mechanical clocks in lieu of pendulums since a weight bouncing on a spring gives simple harmonic motion.
Whenever we see "per second" that's a form of velocity or flow. Per second squared is a form of acceleration (related to force)
I know that because as you know I'm into sundials, but that's more of a gnomonist, albeit I understand physics somewhat, also. A horologist builds and repairs clocks, and as such I do not think many of them are into the theoretical aspect of orbital motion and similar time-related mathematics, but they are into the mechanical aspects of clocks, one being knowledgeable about Hooke's Law. I dabbled a little into clocks, and I collected some and right now have strange clocks working around here.