Upon learning calculus, I decided it was time to derive all of classical mechanics to give myself a good understanding of physics. What I found was that, while trying to do so, I would need some definitions for the more abstract concepts, such as work and energy. What I found was that the definition of work, W = Fs, has weird implications and does not seem intuitively correct as it is based on two variables that affect each other as the system continues.
Work is the least psychologically pleasing (I chose my words carefully) topic in all of physics for me. It implies that it takes more work to move objects that already have a high velocity than objects with velocity 0, but don't different inertial reference frames contradict this definition? i.e. a baseball moving through space at v=a from the reference of a bystander at v=0 would be moving through a lot more space while being accelerated than from the reference of, say, a train that's going at v=a and sees the baseball at v=0.
I want an answer to that question (on the contradiction of the energy formula with different inertial frames), and I'd also like an intuitive explanation of work.