Final answer:
If an object's mechanical energy is equal to its potential energy, the kinetic energy of that object is 0 joules because the total mechanical energy is the sum of kinetic and potential energy which must remain constant in the absence of non-conservative forces.
Step-by-step explanation:
If an object's mechanical energy is equal to its potential energy (PE), this means that the object has no kinetic energy (KE) at that moment. We deduce this from the principle that the mechanical energy of a system is conserved in the absence of non-conservative forces, such as friction or air resistance. Therefore, if mechanical energy equals potential energy, then the equation KE + PE = constant simplifies to 0 + PE = constant, which indicates that KE must be 0 joules because all the mechanical energy is stored as potential energy.