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.

Solving for (constant) acceleration

Time is unknown

$a={\dfrac {v_{f}^{2}-v_{i}^{2}}{2x}}\,$

Final velocity is unknown

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

Initial velocity is unknown

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

Distance is unknown

$a={\dfrac {v_{f}-v_{i}}{t}}\,$

Solving for time

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

$t={\dfrac {v_{f}-v_{i}}{a}}\,$

Solving for final velocity

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

$v_{f}=v_{i}+at\,$

Solving for initial velocity

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

$v_{i}=v_{f}-at\,$

Solving for distance

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

$x=v_{i}t+{\tfrac {1}{2}}at^{2}\,$

Initial velocity is unknown

$x=v_{f}t-{\tfrac {1}{2}}at^{2}\,$