After producing a model, it must be corroborated against reality. The Falling Body Model has been corroborated by a vast number of experiments in which the time and distance were measured and compared according to the formula. In general all models must be corroborated by experiment.
The Falling Body Model can be derived from deeper models, namely Newton's laws of motion and the assertion that, over the limited distances concerned, gravitation exerts a constant acceleration on the object. When the model in question can be derived from other models, it is the other models that are being corroborated by our experiments.
Because nature is not formal, we cannot prove that our models of it are correct. All we can do is test our models against nature's behavior.
Such testing often exposes restrictions on the applicability of our models. For example, the Falling Body Model is inaccurate if air resistance is significant. Thus, we learn not to use that model to predict how long it takes a feather to fall from a 200 foot tower in the earth's atmosphere.
In addition, attempts at corroboration might reveal that the model is actually incorrect. Careful measurements might expose the fact that the gravitational force increases as the body falls closer to earth. Very careful measurements might reveal relativistic effects. Technically, the familiar Falling Body Model is just wrong, even under excessive restrictions such as ``in a perfect vacuum'' and ``over small distances.'' But it is an incredibly useful model nonetheless.
There are several morals here.
Models need not be complete to be useful.
Models need not be perfectly accurate to be useful.
The user of a model must understand its limitations.