Formula: Uniformly Accelerated Motion Velocity Initial velocity Current position Initial position
$$\class{blue}{v(}x\class{blue}{)} ~=~ \sqrt{ {\class{blue}{v_0}}^2 ~+~ 2 \class{red}{a} \,(x - x_0) }$$
$$\class{blue}{v(}x\class{blue}{)} ~=~ \sqrt{ {\class{blue}{v_0}}^2 ~+~ 2 \class{red}{a} \,(x - x_0) }$$
$$\class{blue}{v_0} ~=~ \sqrt{\class{blue}{v}^2 ~-~ 2\class{red}{a}\, (x-x_0)}$$
$$x ~=~ x_0 ~+~ \frac{ \class{blue}{v}^2 - {\class{blue}{v_0}}^2 }{ 2\class{red}{a} }$$
$$x_0 ~=~ x ~-~ \frac{ \class{blue}{v}^2 - {\class{blue}{v_0}}^2 }{ 2\class{red}{a} }$$
$$\class{red}{a} ~=~ \frac{ \class{blue}{v}^2 - {\class{blue}{v_0}}^2 }{ 2(x-x_0) }$$
Velocity
$$ \class{blue}{v} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
Velocity of a body accelerating / decelerating with a constant acceleration \(a\).
Initial velocity
$$ \class{blue}{v_0} $$ Unit $$ \frac{\mathrm m}{\mathrm s} $$
Velocity that the body had at the initial time before it started to accelerate.
Current position
$$ x $$ Unit $$ \mathrm{m} $$
Current position (e.g. end position) of the body on the \(x\) axis.
Initial position
$$ x_0 $$ Unit $$ \mathrm{m} $$
Initial position of the body on the \(x\) axis before it started to accelerate. The difference between the current position and the initial position is the distance traveled: \( s = x - x_0 \).
Acceleration
$$ \class{red}{\boldsymbol a} $$ Unit $$ \frac{\mathrm m}{\mathrm{s}^2} $$
Constant (fixed) acceleration of the body.