Here is one of my ramblings. Please comment and let me know your thoughts. Newtonian mechanics. As a starting point - tale an iron bar say 20cm square and 50m long weighing 1000 kg travelling at 1m per sec. You want to quantify the intrinsic qualities that this system poseses. Stand in front of it , it hits you but doesn't hurt you travel of with the block. So first thoughts are you multiply mas and velocity as these are the only qualities the system have so you think job done. But then you do the same experiment with a smaller block 1kg moving at 1000 m per sec so mv is the same but different outcome your blasted to hell. So you then think I have one value of 1000 this quantity cannot describe the 2 different outcomes. So you surmise that mv is not the only intrinsic qulity the block nce. First give the quality a name call it energy which will be our measure of change. Common sense tells us this new quality has a greater dependence on velocity than on mass. But what is this dependence. I fish about with m and v thinking what the connection is but to work it out I think in the 1m per sec collision I accelerate very slowly in the 1000m per sec collision I accelerate very quickly and here is the crux of it- what do I mean by accelerating quickly or slowly. You can accelerate for a given time over a distance or you could say accelerate ove a giev distance in a certain time. Linguistically these things sound the same but are in fact 2 different things. Consider m to be 1 then force is acceleration so force measured over a time interval gives us mv momentum and force measured over a distance gives you 1/2 mv squared. So these are the 2 intrinsic qualities and they can only be so as there is no other watmy to quantify the application of force eithe over a distance or over a time. If i then ask why should this be then I am into the realms of philosophy not physics.