The same difference in velocity means more KE difference for a faster body. How so?
There’s you, observer A, standing still beside 2 parallel railway tracks. There’s your friend, observer B, on a train doing 100 metres per second. There’s another train (called C)on the 2nd track doing 110 mps in the same direction. C’s mass is 100kg. The formula for KE is e = mass/2 x velocity^2.
B measures C’s velocity as 10mps (relative to B), so if C slows to 100mps (so it’s at rest for B), B will measure the change in C’s KE as 100kg/2 = 50kg x 10^2mps = 50kg x 100mps = 5000 joules. That’s the energy it took C to slow down.
Now, this 5000 joules is a real, fixed quantity. If B could witness C’s fuel consumption he should see 5000j of fuel burned to slow the train. But what do you see, playing the role of observer A?
You see train C with an initial KE of 100kg/2 = 50kg x 110^2mps = 50ks x 12100j = 605,000j. After C has slowed you measure its final KE to be 100kg/2 = 50kg x 100^2mps = 50ks x 10000j = 500,000j. It follows that C needed 605,000 - 500,000 = 105,000j to slow down.
This 105,000 joules is also a real, fixed quantity. It’s the energy C needed to use to slow down. If you could witness C’s fuel consumption you should see 105,000j of fuel burned to slow the train. You should measure the brakes ending up with a higher temperature than B measures. You would see C’s brakes getting white hot and B would see them only getting red hot.
What is it about the world in motion that resolves this contradiction?