A common example of one-dimensional motion is free fall. An object in free fall has an acceleration equal that of gravity; that is, an acceleration equal to that of an object that is dropped and falls straight towards the earth. The acceleration due to gravity near the surface of the Earth is about 9.8 meters per second squared. When dealing with objects in free fall that are moving vertically, it is customary to use "y" rather than "x" to represent their position. Also, the acceleration "a" is replaced with negative "g" since the acceleration will be down, or negative, in direction and equal to "g" in magnitude. Think for a moment about objects in free fall. Aristotle claimed that the acceleration of a falling object depends on its mass, or in other words, that heavier objects fall faster. Galileo disagreed, saying that the acceleration of a falling object is independent of its mass. Who do you think was correct? Let's find out by dropping two objects with different masses from the same height. According to Aristotle, the heavier object should hit the ground first. Galileo would say that the two objects should hit at the same time. Galileo was correct. The speed of a falling object is independent of mass. It is possible to use the equations of motion for an object in free fall to experimentally determine the acceleration due to gravity. Suppose an object falls from an initial height of positive 1.25 meters to the ground, a height of zero. If this free fall takes 0.505 seconds, then what is the object's acceleration? If this free fall takes 0.505 seconds, then what is the object's acceleration? ... The object's velocity increases as it is falling in a negative direction, so the acceleration must be negative. ... Remember that the time is squared. ... Substituting the given values and solving for acceleration gives the predicted value of -9.8 m/s2. ... So, as you have seen, it is possible to describe motion in one dimension with a constant acceleration in a simple yet scientific way using these fundamental equations.

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