Can any object have momentum even if its mechanical energy is 0? explain.

yes i can explain this theoritically as 

let a body has both  P.E and K.E &   P.E = - K.E .  then totol mechanical energy =K.E +P.E =0

but momentum is there as body is having some velocity in this case

but i am not sure if it is practically possible or not as there is no such example striking me right now

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