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So, as I understand, kinetic energy of a moving object is proportional to its velocity squared. So I'm wondering where these inconsistencies come from, and how they are resolved:

So, say two objects of mass M are travelling, with reference to a stationary observer, one in the left hand direction and one in the right hand direction, both at velocity V.

To the stationary observer, they would record the energy of each object as 0.5*M*V^2 correct? Giving a total kinetic energy of M*V^2.

Now, in the same system, but taken from the frame of reference of one of the moving object, it observes the other moving away from it at a velocity of 2*V, and hence it would see the kinetic energy of the system to be 0.5*M*(2V)^2, which I suppose simplifies to 2*M*V^2.

Where does this change in energy come from? Am I making some incorrect assumptions?

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# Kinetic Energy of Objects in System, in different frames of reference.

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