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Application to vertical motion under constant acceleration

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 (-16t2 + bt)' = -32t + b and the corollary we get

y = -16t2 + 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.