How would one prove W = F.s and why would only F.s be conserved (in energy conservation) and why not F.s^2, or F.s^3? One possibility is by experimental observation and verification. But how would one go about it without experimentation?
s = Displacement vector
F = Force vector
and by dot product, we are basically trying to find: (Component of Force along the displacement)*(displacement)
s = Displacement vector
F = Force vector
and by dot product, we are basically trying to find: (Component of Force along the displacement)*(displacement)