Both classical and neo-classical applications of calculus of deformable material bodies are utilized to formulate and to solve a variety of engineering and bio-mathematical problems. The results should help discern various balance and equations of state formulations when combined with experimental validation. The presented calculus has an evolutionary perspective of addressing change, as well as accumulated change in a unified manner to better understand motions and memory described through both quantification and computation. Several original contributions are made on reactive power law fluid flows, on lubrication, on acoustic horn shapes, on dielectric relaxation, as well as on peristaltic pumping. Moreover, new perspectives are given for dissipation contributions in energetics of the motions.