As drops from a dripping faucet fall 1.0 second apart, the distance between them will increase due to the acceleration of gravity. The gravitational force causes each subsequent drop to fall faster than the previous one, leading to greater spacing over time. The equation of motion, s = ut + 0.5at², can be applied to analyze this behavior, where 's' represents distance, 'u' is the initial velocity, and 'a' is acceleration due to gravity. Without mathematical demonstration, the assumption remains that the distance between drops increases. Understanding this concept is crucial for accurately predicting the behavior of falling objects.