Motion Equations

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SUVAT Equations

S: Displacement: m

U: Initial Velocity: $m{s}^{-1}$

V: Final Velocity: $m{s}^{-1}$

A: Acceleration: $m{s}^{-2}$

T: Time: s

$v_{av}=\frac{s}{t}$

$v=u+at$

$s=ut+\frac{1}{2}a{t}^2$

$s=vt+\frac{1}{2}a{t}^2$

$v^2=u^2+2as$

$s=(\frac{u+v}{2})t$

Displacement: m

$s=ut+\frac{1}{2}a{t}^2$

$s=vt+\frac{1}{2}a{t}^2$

$s=\frac{t}{2}(u+v)$

$s=\frac{v^2-u^2}{2a}$

Initial Velocity: $m{s}^{-1}$

$u=v-at$

$u=\frac{s-a{t}^2}{2t}$

$u=\frac{2s}{t}+v$

$u=\sqrt{2as-v^2}$

Final Velocity: $m{s}^{-1}$

$v=u+at$

$v=\frac{s+a{t}^2}{2t}$

$v=\frac{2s}{t}+u$

$v=\sqrt{u^2+2as}$

Acceleration: $m{s}^{-2}$

$a=\frac{v-u}{t}$

$a=\frac{2(vt-s)}{t^2}$

$a=\frac{2(s-ut)}{t^2}$

$a=\frac{v^2-u^2}{2s}$

Time: s

$t=\frac{v-u}{a}$

$t=\frac{v-\sqrt{v^2-2as}}{a}$

$t=\frac{\sqrt{2as+u^2}-u}{a}$

$t=\frac{2s}{u+v}$