2019-2020/1ST/Derivation/Nombre_derive/1E_taux_variation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mon hamster dans sa roue\n",
    "\n",
    "Mon hamster court dans sa roue durant toute la journée. J'aime l'étudier et aujourd'hui je voudrait savoir à quelle vitesse il avance dans sa roue.\n",
    "\n",
    "\n",
    "## Distance parcourue\n",
    "\n",
    "Lors d'anciennes expérimentation, j'ai enregistré sur un jour la position de sa roue. Je peux maintenant y avoir accès par la fonction `position`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from hamster import position, graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fb4f5674790>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
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    }
   ],
   "source": [
    "graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour connaître la position de la roue à un moment donné, je dois le renseigner comme paramètre de la fonction.\n",
    "\n",
    "Par exemple au début de la journée (8h) à `t=0` la position de la roue est à"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "À midi, donc `t=4` la position de la route est à"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "position(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quelle est la position de la roue à 10h (`t=2`)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quelle est la position de la roue à 16h?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quelle est la position de la roue à 8h30?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quelle est la position de la roue à 12h30?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vitesse moyenne\n",
    "\n",
    "Comme je disais au début, ce n'est pas la position de la roue qui m'interesse mais bien la vitesse de mon hamster.\n",
    "\n",
    "Quelle est la **vitesse moyenne** de mon hamster entre 8h et 12h?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quelle est la vitesse moyenne de mon hamster sur la journée entre 8h et 16h?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entre quelles heures, mon hamster s'est-il montré le plus rapide?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme on commence un peu trop souvent écrire le même calcul, c'est qu'il est temps de programmer une fonction pour le faire à notre place.\n",
    "\n",
    "Ci-dessous, il y a le début de la définition de la fonction. À toi de compléter les ... pour que cette fonction calcule la vitesse du hamster entre les deux moments `t1` et `t2`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vitesse(t1,t2):\n",
    "    return ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilise ta nouvelle fonction vitesse pour calculer la vitesse moyenne de mon hamster entre 8h et 12h. Tu devrais trouver le même résultat que plus haut."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vitesse(..., ...)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculer la vitesse de mon hamster entre 11h30 et 12h."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Puis entre 12h et 12h30."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vitesse instantannée\n",
    "\n",
    "Les voitures ont un compteur de vitesse qui donne la **vitesse instantannée** du véhicule pas la vitesse moyenne entre 2 moments.\n",
    "\n",
    "J'aimerai connaître la **vitesse instantannée** de mon hamster à 12h.\n",
    "\n",
    "Pour faire cela, on va calculer la vitesse moyenne un peu avant 12h disons entre 11h45 et 12h puis la vitesse moyenne un peu après entre 12h et 12h15.\n",
    "\n",
    "Calcule ces deux vitesses moyennes sur 15min."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ensuite on recommence mais cette fois-ci avec une vitesse moyenne sur 5minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et on continue avec une amplitude de 1min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour avoir la vitesse instantannée, il faudrait continuer ainsi jusqu'à ce que l'amplitude soit nulle. Les vitesses moyennes se rapprocheraient de plus en plus autour d'une valeur que l'on appelle **vitesse instantannée**.\n",
    "\n",
    "\n",
    "À toi de trouver la vitesse instantannée à 13h."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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