




Given that a falling body obeys the equation
(acceleration of gravity)
we can find an explicit formula for y by using our corollary.
Notice that (y')' = y" and (32t)' = 32 which by the corollary tells us
y' = 32t + b, for b a constant
Using (16t^{2} + bt)' = 32t + b and the corollary we get
y = 16t^{2} + bt + c, for constants b and c.
The constants b and c appearing here have physical interpretations.
They are, respectively, the initial velocity and initial position of the object.