I don't think so.
Counterexample:
Ball A, a 1 kg ball moving forwards at 4 m/s, goes into the back of Ball B, a 1 kg ball moving forwards at 2 m/s.
Ball A changes to move forwards at 2 m/s and Ball B changes to move forwards at 4 m/s.
This would conserve both momentum and kinetic energy.
Counterexample:
Ball A, a 1 kg ball moving forwards at 4 m/s, goes into the back of Ball B, a 1 kg ball moving forwards at 2 m/s.
Ball A changes to move forwards at 2 m/s and Ball B changes to move forwards at 4 m/s.
This would conserve both momentum and kinetic energy.
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