2.   Basis of Classification

The classification follows five organizing considerations:

1. Operational role: What function does an applied force perform within the mechanical operation?
2. Value variation: Does the applied force or velocity value remain the same or change across intervals?
3. Combination: Does the operation involve an individual applied force or a resultant formed from multiple applied forces?
4. Temporal description: Is the quantity being considered at an individual interval or across the complete operation?
5. Travel outcome: How do the interval-specific velocity values contribute to the accumulated travelling distance?

These considerations provide a structured classification without creating additional foundational quantities.

 

The principal relationships used throughout the paper are:

 

𝑓 ∝ 𝑣

𝐹_𝑖 = 𝑓_𝑖𝑡_𝑖

𝑠_𝑖 = 𝑣_𝑖𝑡_𝑖

𝑛

𝐹 = ∑ 𝑓_𝑖 𝑡_𝑖

𝑖=1

𝑛

𝑆 = ∑ 𝑣_𝑖 𝑡_𝑖

𝑖=1

𝑆

𝑉 = 𝑇

𝐹 = 𝑘𝑆

Here, 𝑓𝑖 and 𝑣𝑖represent the applied force and velocity values associated with an interval, while 𝐹and 𝑆represent the accumulated force quantity and travelling distance.