Final answer:
At escape velocity, the kinetic energy of a spacecraft equals its gravitational potential energy, allowing it to achieve a total energy of zero and escape the planet's gravitational influence.
Step-by-step explanation:
When a spacecraft reaches escape velocity, the relationship between the gravitational potential energy (GPE) and kinetic energy (KE) in the system is such that the kinetic energy equals the gravitational potential energy. This is because in order for an object to escape the gravitational pull of a planet without further propulsion, it must have sufficient kinetic energy to do positive work equal to the negative value of gravitational potential energy at that point. This balance allows the total energy to be zero, which indicates an unbound state, as the object will not return to the gravitational influence of the planet.
To further clarify, objects that are bound (e.g., in an orbit around a planet) have a total energy that is less than zero, while an object that is unbounded (e.g., having enough energy to escape the gravitational influence of a planet) has a total energy of zero or greater. Therefore, the correct description of the energy relationship when a spacecraft reaches escape velocity is that the kinetic energy equals the gravitational potential energy.