I know where the formula of work comes from and how we get it using integration. The work formula is interesting but it was counter-intuitive for me to choose it to quantify energy. Instead I was inclined to state that energy should be F.t Is it in order to better fit the concept of potential energy? Moreover with work and kinetic energy as a scale, another counter-intuitive concept gave me trouble is that power (of an engine for instance) increases as time passes. If I use the same amount of fuel over time to produce a constant force on an object, whatever the velocity it gains, why would my instataneous power should be higher if I don't spend more energy in the process? I would have been inclined to use the constant jerk instead. I know that momentum are conserved (I can't explain why) and that a part of kinetic energy is converted and lost into thermic form. But I still don't get what lead us on the right track. I can't just swallow it whithout knowing what it is.
I don't want to define a new type of energy. I know we can't just choose as we wish. Momentum as energy scale to describe transmission of energy in all physics phenomena, would have been linearly proportional to velocity whereas kinetic energy as defined today is not linear to it. Therefore we have two really different function growth in respect to displacement and time, two different degree which means that no constant can connect them.
How come momentum is really conserved for two object. Does it not fail to account for the heat produced in a collision (known as coming from the extra amount out of the V² of the kinetic formula), the heat which can be seen as many little particles colliding, each having a momentum too, momentum created though conserved?!