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It seems to me that John M. is asking (see below) "what
should happen in an impossible situation?". In Jim's frame
of reference the 2 kg block can not possibly be at rest,
unless it is not only a collision of two objects.
John Mallinckrodt wrote:
.... so let me ask you to answer the following question:
A 2 kg block and a 1 kg block head toward each other with equal
and opposite velocities of magnitude 1 m/s. After colliding, the
2 kg block is at rest. How much work was done on the 1 kg block