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--git a/TST_sti2d/01_Derivation/exercises.tex b/TST_sti2d/01_Derivation/exercises.tex index 51e546f..ea56793 100644 --- a/TST_sti2d/01_Derivation/exercises.tex +++ b/TST_sti2d/01_Derivation/exercises.tex @@ -1,10 +1,61 @@ \collectexercises{banque} -\begin{exercise}[subtitle={<++>}, step={1}, origin={<++>}, topics={Dérivation}, tags={Dérivation}] - <++> +\begin{exercise}[subtitle={Balistique}, step={1}, origin={Création}, topics={Dérivation}, tags={Dérivation, Physique, Tache complexe}] + Le gouvernement est inquiet. Un état ennemie a tiré un projectile en sa direction. Sa trajectoire a été a été enregistrée et est représentée sur les 2 graphiques ci-dessous. Le premier représente la distance au sol de l'objet en fonction du temps et le deuxième sa hauteur en fonction du temps. + + + \begin{tikzpicture}[baseline=(a.north), xscale=0.5, yscale=0.5] + \tkzInit[xmin=0,xmax=14,xstep=1, + ymin=0,ymax=3600,ystep=500] + \tkzGrid + \tkzAxeXY + \tkzFct[color=red,very thick,% + ]{294*\x}; + \end{tikzpicture} + \begin{tikzpicture}[baseline=(a.north), xscale=0.5, yscale=0.35] + \tkzInit[xmin=0,xmax=14,xstep=1, + ymin=0,ymax=200,ystep=20] + \tkzGrid + \tkzAxeXY + \tkzFct[color=red,very thick,% + %domain=0:12.2 + ]{-4.9*\x**2+60*\x}; + \end{tikzpicture} + + \begin{enumerate} + \item Combien de temps le projectile est-il resté en l'air? + \item Quelle distance a été parcouru? + \item À quelle hauteur le projectile est il allé au maximum? + \end{enumerate} + + Le projectile n'a visiblement pas été tiré dans des conditions optimales. Pour évaluer les risques encourus, les généraux ont besoin de connaître la vitesse horizontale et la vitesse verticale au moment du lancement. + + \begin{enumerate} + \setcounter{enumi}{3} + \item Déterminer la vitesse horizontale au moment du lancement. + \item Même question pour la vitesse verticale. + \end{enumerate} + À partir de ces informations, il est possible de connaître la portée maximale du projectile. Mais il vous manque encore des outils de physique! Rendez-vous à la fin de l'année! \end{exercise} -\begin{solution} - <++> -\end{solution} +\begin{exercise}[subtitle={Réaction chimique autocatalytique}, step={1}, origin={Création}, topics={Dérivation}, tags={Dérivation}] -\collectexercisesstop{banque} \ No newline at end of file + \begin{minipage}{0.5\textwidth} + Une réaction autocatalytique est une réaction chimique dont le catalyseur figure parmi les produits de la réaction. On concidère une telle réaction où deu élément A et B réagissent pour donner deux B. L'évolution de la concentration de B au cours de l'expérience est donnée par le graphique ci-contre. + \medskip + + En vous inspirant de l'exercice précédent, définir la vitesse d'une réaction chimique. Puis déterminer le moment où la réaction chimique est le plus rapide ainsi que sa vitesse. + \end{minipage} + \hfill + \begin{minipage}{0.4\textwidth} + \begin{tikzpicture}[baseline=(a.north), xscale=1, yscale=0.6] + \tkzInit[xmin=0,xmax=5,xstep=1, + ymin=0,ymax=5,ystep=1] + \tkzGrid + \tkzAxeXY + \tkzFct[color=red,very thick]% + {1/(1+exp(x)}; + \end{tikzpicture} + \end{minipage} +\end{exercise} + +\collectexercisesstop{banque} diff --git a/TST_sti2d/01_Derivation/index.rst b/TST_sti2d/01_Derivation/index.rst index 44e2bc8..56d014f 100644 --- a/TST_sti2d/01_Derivation/index.rst +++ b/TST_sti2d/01_Derivation/index.rst @@ -15,6 +15,10 @@ Temps: 1h30 On construit la notion de vitesse instantanée puis celle de débit instantanée avec une approche plutôt physique. +.. image:: ./1E_vitesse.pdf + :height: 200px + :alt: Vitesse et vitesse de réaction chimique. + Il faudra inciter les élèves à utiliser les notations avec delta pour faire la transition vers la notation physique de la dérivée. On en profitera alors pour montrer les 3 notations de la dérivée. Cours: Vitesse/débit sur un intervalle de temps et instantanée.