User:Rainmonger/Physics equations

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[edit] Kinematics

Many kinematics problems are given to students in high school and college physics courses which involve the five following measurable quantities of a body in motion:

$a\,$ - acceleration (most often assumed to be constant)
$t\,$ - time elapsed
$v_f\,$ - final velocity (this variable may also be represented by just $v\,$ )
$v_i\,$ - initial velocity (this variable may also be represented by $u\,$ )
$x\,$ - distance traveled (this variable may also be represented by $d\,$ or $s\,$ )

If one knows any three of the above quantities for a given situation, then one may solve for any of the other two. The equations below demonstrate this property.

[edit] Solving for (constant) acceleration

[edit] Time is unknown

$a=\dfrac{v_f^2-v_i^2}{2x}\,$

[edit] Final velocity is unknown

$a=2\dfrac{x-v_it}{t^2}\,$

[edit] Initial velocity is unknown

$a=2\dfrac{v_ft-x}{t^2}\,$

[edit] Distance is unknown

$a=\dfrac{v_f-v_i}{t}\,$

[edit] Solving for time

[edit] Acceleration is unknown (but constant)

$t=\dfrac{2x}{v_f+v_i}\,$

[edit] Final velocity is unknown

$t=\dfrac{-v_i+\sqrt{v_i^2+2ax}}{a}\,$

[edit] Initial velocity is unknown

$t=\dfrac{v_f+\sqrt{v_f^2+2ax}}{a}\,$

[edit] Distance is unknown

$t=\dfrac{v_f-v_i}{a}\,$

[edit] Solving for final velocity

[edit] Acceleration is unknown (but constant)

$v_f=\dfrac{2x}{t}-v_i\,$

[edit] Time is unknown

$v_f=\sqrt{v_i^2+2ax}\,$

[edit] Initial velocity is unknown

$v_f=\dfrac{2x+at^2}{2t}\,$

[edit] Distance is unknown

$v_f=v_i+at\,$

[edit] Solving for initial velocity

[edit] Acceleration is unknown (but constant)

$v_i=\dfrac{2x}{t}-v_f\,$

[edit] Time is unknown

$v_i=\sqrt{v_f^2-2ax}\,$

[edit] Final velocity is unknown

$v_i=\dfrac{2x-at^2}{2t}\,$

[edit] Distance is unknown

$v_i=v_f-at\,$

[edit] Solving for distance

[edit] Acceleration is unknown (but constant)

$x=\dfrac{v_f+v_i}{2}t\,$

[edit] Time is unknown

$x=\dfrac{v_f^2-v_i^2}{2a}\,$

[edit] Final velocity is unknown

$x=v_it+\tfrac{1}{2}at^2\,$

[edit] Initial velocity is unknown

$x=v_ft-\tfrac{1}{2}at^2\,$

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