Main variables:

Main Equations:

Motion with constant velocity:

\begin{equation*}
\vec{x}_f = \vec{x}_i + \vec{v}_i t.
\end{equation*}

Displacement:

\begin{equation*}
\Delta \vec{x} = \vec{x}_f – \vec{x}_i.
\end{equation*}

Distance:

\begin{equation*}
|\Delta \vec{x}|.
\end{equation*}

Average velocity:

\begin{equation*}
\vec{v}_{av} = \frac{\vec{x}_2 – \vec{x}_1}{t_2 – t_1} = \frac{\Delta \vec{x}}{\Delta t}.
\end{equation*}

Instantaneous velocity:

\begin{equation*}
\vec{v}_{ins} = \lim_{\Delta t \rightarrow 0} \frac{\Delta \vec{x}}{\Delta t} = \frac{d\vec{x}}{dt}.
\end{equation*}

Average acceleration:

\begin{equation*}
\vec{a}_{av} = \frac{\vec{v}_2 – \vec{v}_1}{t_2 – t_1} = \frac{\Delta \vec{v}}{\Delta t}.
\end{equation*}

Instantaneous acceleration:

\begin{equation*}
\vec{a}_{ins} = \lim_{\Delta t \rightarrow 0} \frac{\Delta \vec{v}}{\Delta t} = \frac{d\vec{v}}{dt}.
\end{equation*}

Motion with constant acceleration:

\begin{equation*}
\vec{x}_f = \vec{x}_i + \vec{v}_i t + \frac{1}{2} \vec{a} t^2.
\end{equation*}

Velocity as a function of time:

\begin{equation*}
\vec{v}_f = \vec{v}_i + \vec{a} t.
\end{equation*}

Velocity as a function of the position and the acceleration:

\begin{equation*}
|\vec{v}_f^2| = |\vec{v}_i^2| + 2 \vec{r} \cdot \vec{a}.
\end{equation*}

Motion with constant acceleration as a function of the velocities:

\begin{equation*}
x = x_0 + \frac{1}{2} (v_i + v_f) t.
\end{equation*}