Editing Free fall (section)

=== Uniform gravitational field without air resistance ===
This is the "textbook" case of the vertical motion of an object falling a small distance close to the surface of a planet. It is a good approximation in air as long as the force of gravity on the object is much greater than the force of air resistance, or equivalently the object's velocity is always much less than the terminal velocity (see below).{{Citation needed|date=April 2025}}

[[File:Free-fall.gif|right|100px|Free-fall|alt=Free-fall alt.//vel.?|border]]
:<math>v(t)=v_{0}-gt\,</math> and

:<math>y(t)=v_{0}t+y_{0}-\frac{1}{2}gt^2 ,</math>

where
:<math>v_{0}\,</math> is the initial vertical component of the velocity (m/s).
:<math>v(t)\,</math> is the vertical component of the velocity at <math>t\,</math>(m/s).
:<math>y_{0}\,</math> is the initial altitude (m).
:<math>y(t)\,</math> is the altitude at <math>t\,</math>(m).
:<math>t\,</math> is time elapsed (s).
:<math>g\,</math> is the acceleration due to [[gravity]] (9.81 m/s<sup>2</sup> near the surface of the earth).
If the initial velocity is zero, then the distance fallen from the initial position will grow as the square of the elapsed time:

<math>v(t)=-gt</math> and <math>y_{0}-y(t)=\frac{1}{2}gt^2.</math>

Moreover, because [[square number#Properties|the odd numbers sum to the perfect squares]], the distance fallen in successive time intervals grows as the odd numbers. This description of the behavior of falling bodies was given by Galileo.<!-- posthumous publ. --><ref>{{Cite book |last1=Olenick |first1=R.P. |url=https://books.google.com/books?id=xMWwTpn53KsC&pg=PA18 |title=The Mechanical Universe: Introduction to Mechanics and Heat |last2=Apostol |first2=T.M. |last3=Goodstein |first3=D.L. |publisher=Cambridge University Press |year=2008 |isbn=978-0-521-71592-8 |page=18 |language=en}}</ref>