This might be a silly question, that doesn't make sense, but I'll post

[aaaa202]

This might be a silly question, that doesn't make sense, but I'll post it anyways...
When you escape a uniform force field, the greater velocity you have to start with, the less will the total decrease in velocity be since Ekin is proportional to v squared. Now if you want to understand this using kinematic terms, it would be that, the less velocity you have the longer time you will be under the influence of the acceleration of the force field and thus "lose" more velocity.
Now, since this has then something to do with time, why is it, that it is, the energy that determines the decrease in velocity. Because I have always learned that energy is something that has to do with the space, while impulse has something to do with time. i.e. one is integrated over space other over time. I think analytical mechanics will later give me a more fundamental understanding of all this, but could someone meanwhile tell me why it's not wrong at all, that energy determines the total decrease in velocity.

 

[Naty1]

Conservation of energy applies to your example but not conservation of momentum.

for example, rising from the Earth and returning , total KE and PE remains constant neglecting friction.

 

[aaaa202]

yes yes, that I totally get. But I thought the kinematic interpretation is just something with time, so thus I don't see why that should match using energy conservation that has something to with the force over a distance..