kinetic energy of an object is zero when momentum is zero
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Momentum of an object , P = mv
If P = 0
⇒v=0
This is because mass of the can never be 0. Now , kinetic energy of the object ,
K= 1/2×m×v²
Since , V = 0
⇒K=0
Hence, when the object has zero momentum, its kinetic energy is also zero.
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