\documentclass[convert=true,convert={convertexe={convert},density=1200,outext=.png}]{standalone}

\input{figsDefs.tex}

\begin{document}
	
\begin{tikzpicture}%
	% trajectoire f=1./48.*(-2*x*x*x-9*x*x+107)
	% deriv\'{e}e fp=1./48.*(-6*x*x-18*x)
	\shorthandoff{:}
	\draw[-,blue,thick] plot[id=temp,smooth,domain=-1:3.2,samples=30] function{1./48.*(-2*x*x*x-9*x*x+107)} node[right=3pt] {$\Gamma$};
	\shorthandon{:}
	% point 1
	\pgfmathsetmacro{\valX}{1};
	\pgfmathsetmacro{\valY}{1./48.*(-2*\valX*\valX*\valX-9*\valX*\valX+107)};
	\path (\valX,\valY) node[shape=coordinate] (P1) {};%(1,2)%(-1,2.083333)
	%\draw[blue,fill=blue] (P1) circle (0.05) node[above] {$P_1$};%
	\draw[->,>=latex,thick] (0,0) -- (P1) node[left,pos=0.5] {$\vec{r}_1$};%
	% tangente
	\pgfmathsetmacro{\valPenteUn}{1./48.*(-6*\valX*\valX-18*\valX)};
	\draw[dashed,brown] (P1)+(-1*2,-\valPenteUn*2) -- node[above,sloped,pos=0.2] {} +(1*3,\valPenteUn*3);%
	% vitesse
	\path (1*2,\valPenteUn*2) node[shape=coordinate] (v1) {};
	\draw[->,>=latex,thick,vitCol] (P1) -- +(v1) node[above,pos=0.7] {$\vec{v}_1$};%
	% point 2
	\pgfmathsetmacro{\valX}{1.2};
	\pgfmathsetmacro{\valY}{1./48.*(-2*\valX*\valX*\valX-9*\valX*\valX+107)};
	\path (\valX,\valY) node[shape=coordinate] (P2) {};
	%\draw[blue,fill=blue] (P2) circle (0.05) node[right] {$P_2$};%
	\draw[->,>=latex,thick] (0,0) -- (P2) node[below right,pos=0.5] {$\vec{r}_2$};%
	% tangente
	\pgfmathsetmacro{\valPenteDeux}{1./48.*(-6*\valX*\valX-18*\valX)};
	%%% pente inutile
	%%%\draw[dashed,cyan] (P2)+(-1*1,-\valPenteDeux*1) -- node[above,sloped,pos=0.2] {} +(1*2.5,\valPenteDeux*2.5);%
	% vitesse
	%\path (1*1.9,\valPenteDeux*1.9) node[shape=coordinate] (v2) {};
	\path (1*1.6,\valPenteDeux*1.6) node[shape=coordinate] (v2) {};
	\draw[->,>=latex,thick,vitCol] (P2) -- +(v2) node[below,pos=1] {$\vec{v}_2$};%
	% d\'{e}placement
	%\path (P1) -- (P2) node[above,pos=0.5] {$\Delta\vec{r}$};%
	% origine
	\draw[-] (0,-.1) -- (0,+.1) node[below left,pos=0.6] {$O$};%
	\draw[-] (-.1,0) -- (.1,0) node[below] {};%
	% acc\'{e}l\'{e}ration
	\path ($(v2)-(v1)$) node[shape=coordinate] (Dv) {};
	% support
	\draw[dashed,brown] ($(P1)+5*(Dv)$) -- node[above,sloped,pos=0.7] {support de $\vec{a}$} ($(P1)-10*(Dv)$);%
	\draw[->,>=latex,thick,accCol] (P1) -- ($(P1)+4*(Dv)$) node[below,pos=0.7] {$\vec{a}$};%
	\draw[->,>=latex,thick,vitCol] (P1) -- +(Dv) node[above right,pos=0.5] {};%
	\draw[vitCol] (P1)+(0,.4) node {$\Delta\vec{v}$};
\end{tikzpicture}%

\end{document}