piecewise const acc

A piecewise-constant acceleration is constant over extended time intervals and changing in value discontinuously from one interval to the next.
This is physically unrealistic in any real-life situation, since the acceleration would be expected to change more or less smoothly from instant to instant.
In realistic models of collisions the acceleration changes smoothly, but it still can be approximated as continuous for simplification.

Christopher Duston (ed), "Acceleration", in Conservation Laws, Newton's Laws, and Kinematics, Merrimack College, University of Arkansas, 1 Nov 2023, (), url https://phys.libretexts.org/@go/page/63251 [20250224].