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 Summary

Consider a particle moving at velocity v1 in a straight line. If it were to receive a boost so that its velocity increases to a new higher velocity v2, the change in its kinetic energy as measured by a stationary observer would be 1/2 m (v2^2  v1^2).
However, if we consider an observer moving at a velocity v1 next to the particle, the relative velocity of the particle changes from 0 initially to (v2  v1), so its change in kinetic energy as measured by this observer is 1/2 m (v2  v1)^2.
These quantities are evidently not equal unless v_{1} = v_{2}, but surely the change in kinetic energy should be the same in different frames of reference? I was wondering what mistake or misconception I have made because this has been bugging me for a little while.
Thank you in advance!
Thank you in advance!
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