Editing Kinematics

''Kinematics'' is the study of a body's motion without concern to the forces that act upon it.  

== Displacement ==
A body's ''displacement'' is its change in position from some initial point of reference.  Displacement is defined the difference between that body's current position <math display="inline">x</math> and its initial position <math>x_0</math>, such that:

<math display="block">s = x - x_0</math>

Where <math>s</math> is the displacement of the body, which may also be expressed as <math>\Delta x</math>.  Additionally, in constant acceleration, a body's displacement may also be expressed as:

<math display="block">\begin{align}
s &= v_0 t + \frac{1}{2} a t^2 \\
&= \frac{1}{2} \left(v_0 + v\right)t
\end{align}</math>

Where <math display="inline">a</math> is the acceleration, <math>v</math> is the velocity, <math>v_0</math> is the initial velocity, and <math>t</math> is the time.  

== Velocity ==
A body's ''velocity'' is the rate at which it is displaced over a given interval of time.  Therefore, the velocity <math>v</math> is proportional to the displacement <math>\Delta x</math> and change in time <math>\Delta t</math>, such that:

<math display="block">v = \frac{\Delta x}{\Delta t}</math>

The velocity at a given moment for a body experiencing some acceleration <math>a</math> over a period of <math>t</math> starting at some velocity <math>v_0</math> is given by:

<math display="block">v = v_0 + a t</math>

Additionally, when displacement <math>s</math> is known, the velocity is given by:

<math display="block">v^2 - v_0^2 = 2 a s</math>

== Acceleration ==
A body's ''acceleration'' is the rate at which an object's velocity changes over a given interval of time.  Thus, the acceleration <math>a</math> is given by the change in velocity <math>\Delta v</math> over an interval <math>\Delta t</math>, such that:

<math display="block">a = \frac{\Delta v}{\Delta t}</math>
[[Category:Kinematics]]