Equations (21)-(23) can easily be modified to deal with the
special case of an object free-falling under gravity:

Here, is the downward acceleration due to gravity, is the distance the object has moved vertically between times and (if then the object has risen meters, else if then the object has fallen meters), and is the object's instantaneous velocity at . Finally, is the object's instantaneous velocity at time .

Let us illustrate the use of Eqs. (24)-(26). Suppose that
a ball is released from rest and allowed to fall under the influence of gravity.
How long does it take the ball to fall meters? Well, according to Eq. (24)
[with (since the ball is released from rest), and (since we wish the
ball to *fall* meters)], , so the time of fall is

Suppose that a ball is thrown vertically upwards from ground level with velocity .
To what height does the ball rise,
how
long does it remain in the air, and with what velocity does it strike the
ground? The ball attains its maximum height when it is momentarily at rest
(*i.e.*, when ). According to Eq. (25) (with ),
this occurs at time . It follows from Eq. (24) (with
, and ) that the maximum height of the ball
is given by

(28) |

(29) |