Call me a brainlet, but I don't really understand kinetic energy. When the speed of an object doubles, the kinetic energy is supposed to quadruple.
So when I needed 100J to accelerate an object to 10m/s, I would need an additional 300J to further accelerate it to 20m/s.
But when another object would move in the same direction with the same 10m/s, the speed and kin. energy relative to the object would be zero, so further accelerating it by 10m/s in the same direction observing from the other moving object would acc. it from 0m/s to 10m/s (so 10m/s to 20m/s observing from the ground), which should require only 100J instead of 300 for exactly the same thing.
Another example: I accelerate two objects to 10m/s directly towards each other using 100J for each. When they crash, they have a speed of 20m/s relative to each other, so if they completely stop each other and transform all the energy to heat/deformation etc., they should release 400J, which is more than I initially put in...
What am I doing wrong? Can someone explain?