- #1

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For low velocities, the formula for energy boils down to the classical E=1/2m*v^2

So let's say two astronauts A and B are in empty space absent of gravity.

B has a jetpack and accelerates to 5m/s which require E=1/2m*v^2= 1/2*100kg*(5m/s^2) = 1250 joule

When B is finished accelerating, he finds another astronaut C right next to him (doesn't matter how he got there, he just is).

B and C are moving at 5m/s relative to A. They can both consider themselves at rest according to SR.

So B decides to accelerate again to 5m/s relative to C, requiring again 1250 joule.

For such low velocities, we can add the velocities in the classical sense. So B would see A moving at 10m/s relative to himself with a total of 2500 joules used.

But it requires 1/2*100kg*(10m/s)^2 = 5000 joules to accelerate to 10m/s. So where is my confusion?