Editing Acceleration (section)

===Uniform acceleration===
{{See also|Torricelli's equation}}
[[File:Strecke und konstante Beschleunigung.png|thumb|Calculation of the speed difference for a uniform acceleration]]
''Uniform'' or ''constant'' acceleration is a type of motion in which the [[velocity]] of an object changes by an equal amount in every equal time period.

A frequently cited example of uniform acceleration is that of an object in [[free fall]] in a uniform gravitational field. The acceleration of a falling body in the absence of resistances to motion is dependent only on the [[gravitational field]] strength [[standard gravity|{{math|g}}]] (also called ''acceleration due to gravity''). By [[Newton's second law]] the [[force]] <math> \mathbf{F_g}</math> acting on a body is given by:
<math display="block"> \mathbf{F_g} = m  \mathbf{g}.</math>

Because of the simple analytic properties of the case of constant acceleration, there are simple formulas relating the [[Displacement (vector)|displacement]], initial and time-dependent [[velocity|velocities]], and acceleration to the [[time in physics|time elapsed]]:<ref>{{cite book |title=Physics for you: revised national curriculum edition for GCSE |author =Keith Johnson |publisher=Nelson Thornes |year=2001 |edition=4th |page=135 |url=https://books.google.com/books?id=D4nrQDzq1jkC&q=suvat&pg=PA135 |isbn=978-0-7487-6236-1}}</ref>
<math display="block">\begin{align}
\mathbf{s}(t) &= \mathbf{s}_0 + \mathbf{v}_0 t + \tfrac{1}{2} \mathbf{a}t^2 = \mathbf{s}_0 + \tfrac{1}{2} \left(\mathbf{v}_0 + \mathbf{v}(t)\right) t \\
\mathbf{v}(t) &= \mathbf{v}_0 + \mathbf{a} t \\
{v^2}(t) &= {v_0}^2 + 2\mathbf{a \cdot}[\mathbf{s}(t)-\mathbf{s}_0],
\end{align}</math>

where
* <math>t</math> is the elapsed time,
* <math>\mathbf{s}_0</math> is the initial displacement from the origin,
* <math>\mathbf{s}(t)</math> is the displacement from the origin at time <math>t</math>,
* <math>\mathbf{v}_0</math> is the initial velocity,
* <math>\mathbf{v}(t)</math> is the velocity at time <math>t</math>, and
* <math>\mathbf{a}</math> is the uniform rate of acceleration.

In particular, the motion can be resolved into two orthogonal parts, one of constant velocity and the other according to the above equations.  As [[Galileo]] showed, the net result is parabolic motion, which describes, e.g., the trajectory of a projectile in vacuum near the surface of Earth.<ref>{{cite book |title=Understanding physics |author1=David C. Cassidy |author2=Gerald James Holton |author3=F. James Rutherford |publisher=Birkhäuser |year=2002 |isbn=978-0-387-98756-9 |page=146 |url=https://books.google.com/books?id=iPsKvL_ATygC&q=parabolic+arc+uniform-acceleration+galileo&pg=PA146}}</ref>