User:Rainmonger/Physics equations

One-Dimensional 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 $$u\,$$ or $$v_0\,$$)
 * $$x\,$$ - 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.

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

Final velocity is unknown
$$a=2\dfrac{x-v_it}{t^2}\,$$

Initial velocity is unknown
$$a=2\dfrac{v_ft-x}{t^2}\,$$

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

Acceleration is unknown (but constant)
$$t=\dfrac{2x}{v_f+v_i}\,$$

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

Initial velocity is unknown
$$t=\dfrac{-v_f+\sqrt{v_f^2-2ax}}{-a}\,$$

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

Acceleration is unknown (but constant)
$$v_f=\dfrac{2x}{t}-v_i\,$$

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

Initial velocity is unknown
$$v_f=\dfrac{2x+at^2}{2t}\,$$

Distance is unknown
$$v_f=v_i+at\,$$

Acceleration is unknown (but constant)
$$v_i=\dfrac{2x}{t}-v_f\,$$

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

Final velocity is unknown
$$v_i=\dfrac{2x-at^2}{2t}\,$$

Distance is unknown
$$v_i=v_f-at\,$$

Acceleration is unknown (but constant)
$$x=\dfrac{v_f+v_i}{2}t\,$$

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

Final velocity is unknown
$$x=v_it+\tfrac{1}{2}at^2\,$$

Initial velocity is unknown
$$x=v_ft-\tfrac{1}{2}at^2\,$$