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Here is a possible mechanism. Suppose that the 2 kg block (moving
initially to the right) has a little spring attached, facing the 1 kg
block . The spring is compressed by a correct amount. The trigger which
keeps the spring compressed is release during the collision. Its elastic
energy is used to stop the 2 kg block and to push the 1 kg block to the
right at v=1 m/s. Or it can be a source of chemical energy , such as
nitroglycerine, in right amount.