Not always... say the PE IS -1 and its velocity is 1 m/s... then its mechanical energy is 0 but it has momentum mv!

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Theoretically the gravitational or other potential energies of binding are defined to be negative.  The kinetic energy is always positive.

For a body that has velocity equal to escape velocity from Earth (or any planet) has a total total energy (KE + gravitational PE) zero. All the inter-planetary satellite/space craft missions use this principle.

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