What type of energy is a factor of both weight and speed in door operation?

Kinetic energy is indeed related to both weight and speed in the context of door operation. It is defined as the energy an object has due to its motion, which depends on both the mass (or weight) of the object and its velocity (or speed). In the case of elevator doors, when they move to open or close, their weight contributes to the total energy involved in the operation. The faster the doors move, the more kinetic energy they possess.

Mechanical energy is a broader term that encompasses both potential and kinetic energy, but in this specific context, where the focus is on the motion of the doors and their relationship to weight and speed, kinetic energy is the most relevant type. Therefore, while mechanical energy could describe overall energy in a system involving both types, kinetic energy is specifically tied to the movement of the doors and how their speed increases with their weight.