What physical concept explains the speed of an object at various heights in a vertical drop?

The speed of an object at various heights in a vertical drop is explained by the principle of energy conservation. This principle states that the total mechanical energy of an object remains constant if only conservative forces, like gravity, are acting on it.

As the object is released from a height, its gravitational potential energy, which is dependent on its height above the ground, converts into kinetic energy as it falls. At the top of the drop, the object has maximum potential energy and minimal kinetic energy since it is momentarily at rest. As it descends, its height decreases, leading to a decrease in potential energy and a corresponding increase in kinetic energy, which accounts for the increase in speed.

Thus, by the time the object reaches the bottom of the drop, its potential energy is converted entirely into kinetic energy (ignoring any losses), allowing us to determine its speed at various heights during its fall through the conservation of mechanical energy.