I've asked this once before, but it didn't word it well and didn't get the answer I was looking for, so here is my question:
Imagine you are in a vacuum and friction acting on the object you are pushing is negligible:
If you increase something's speed from 0 to 10 m/s it uses a certain amount of energy (e) and a certain amount of force (f) applied over t time. If you increase it's speed from 10 to 20 m/s it takes f force over t time again, but uses >1e energy since ke = 1/2mv^2. If the force is constant, then the stress on your arm pushing the object is constant, so how does the extra energy get into the object being pushed? If it transferred through your arm then why would the stresses on your arm not increase?