Potential energy equals kinetic energy in certain situations, particularly in the context of mechanical systems involving gravitational forces. A classic example is a pendulum. When the pendulum swings, its energy transforms between potential and kinetic.
At the highest point of the swing, all the energy is gravitational potential energy because the pendulum is momentarily at rest. As it swings downwards, this potential energy converts into kinetic energy, the energy of movement. When the pendulum reaches its lowest point, all the energy is now kinetic.
The specific moment when potential energy equals kinetic energy occurs when the pendulum is at the midpoint of its swing. At this point, the energy has transitioned; half of the total energy is in the form of potential energy, and the other half is kinetic. So, to summarize, potential energy equals kinetic energy when the total energy in the system is evenly divided between the two forms of energy, such as in the midpoint of a swing or any mechanical system where energy conversion is occurring.