The equations of motion can be used only when acceleration is constant.
Free fall is a great example of motion with a constant acceleration. For acceleration to occur, there must be a force acting on an object. Free falling objects have only the force of gravity acting on them (if we ignore air resistance) so the acceleration of a free falling object will be equal to the acceleration due to gravity. Acceleration due to gravity is a constant and so instead of using the symbol, a, for acceleration, we use the symbol, g, for acceleration due to gravity.
We can use the 2nd equation of motion to determine the distance that an object fell if we know how long it took the object to hit the ground. As long as the object was simply dropped or simply falls without additional force throwing it downwards, we can assume the initial velocity of the object is zero. We can simplify the second equation of motion to be used for free fall,
This is the second equation of motion with a couple of changes. We are using y instead of x because the object is moving downwards. Also, we are using the symbol, g, instead of a because the acceleration of the symbol, a, falling object is the acceleration due to gravity.