{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Xocs inelàstics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Dos cotxes amb massa m= 1000 kg circulen a 60 km/h i xoquen frontalment, quedant aturats. Calculeu   \n",
    " a) L'energia alliberada en forma de calor per a cada cotxe.   \n",
    " b) Els temps de frenada si els frens a cada cotxe exerceixen una força constant F = 4 kN   \n",
    " c) L'espai recorregut en aquesta frenada   \n",
    " d) Repetiu els apartats anteriors si la velocitat fos el doble (120 km/h) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solució"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Veiem que podem fer amb el que sabem de teoria. \n",
    "\n",
    "A l'apartat *(a)* es tracta d'un xoc inelàstic amb velocitat final = 0 m/s on tota l'energia cinètica es dissipa en forma de calor:\n",
    "\n",
    "$Q = \\Delta E = Ec(v=v0)$   \n",
    "\n",
    "$Ec = \\frac{1}{2} \\cdot m \\cdot v^{2}$\n",
    "\n",
    "A l'apartat *(b)* tenim un M.U.A. amb acceleració negativa que acaba al repòs:\n",
    "\n",
    "$F = m \\cdot a \\Rightarrow  a = \\frac{F}{m}$\n",
    "\n",
    "$v = v_{0} + a \\cdot t$\n",
    "\n",
    "$\\Delta r = v_{0} \\cdot t + \\frac{1}{2}\\cdot a \\cdot t^{2}$\n",
    "\n",
    "Per tant, sembla que introduïnt les dades a les fòrmules tenim resolt el nostre problema\n",
    "\n",
    "Anem a la pràctica ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Treballant amb unitats a python. La llibreria *pint*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La llibreria *pint* ens permet treballar amb unitats, fer conversions i donar més rigor als càlculs   \n",
    "Teniu un bon tutorial a https://pint.readthedocs.io/en/0.13/tutorial.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pint import UnitRegistry\n",
    "ureg = UnitRegistry()\n",
    "m = 1000 * ureg.kg\n",
    "v0 = 60 * ureg.km / ureg.hour"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El primer pas seria tenir les dades en Sistema Internacional. Fixeu-vos que la llibreria *pint* s'encarrega d'això.   \n",
    "Si bé v0 el tenim en $\\frac{km}{h}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "60.0 kilometer/hour"
      ],
      "text/latex": [
       "$60.0\\ \\frac{\\mathrm{kilometer}}{\\mathrm{hour}}$"
      ],
      "text/plain": [
       "60.0 <Unit('kilometer / hour')>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sempre podem convertir una dada al Sistema Internacional amb `.ito_base_units()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "16.666666666666668 meter/second"
      ],
      "text/latex": [
       "$16.666666666666668\\ \\frac{\\mathrm{meter}}{\\mathrm{second}}$"
      ],
      "text/plain": [
       "16.666666666666668 <Unit('meter / second')>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0.ito_base_units()\n",
    "v0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podem millorar l'expressió gestionan el format de sortida:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Velocitat inicial en S.I: 16.666666666666668 m/s'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'Velocitat inicial en S.I: {:P~}'.format(v0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si haguessim fet nosaltres mateixos la conversió obtindriam el mateix valor:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "16.666666666666668 meter/second"
      ],
      "text/latex": [
       "$16.666666666666668\\ \\frac{\\mathrm{meter}}{\\mathrm{second}}$"
      ],
      "text/plain": [
       "16.666666666666668 <Unit('meter / second')>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0 = 60 * ureg.km / ureg.hour\n",
    "v0 = v0 * 1000 * ureg.m / ureg.km * ureg.hour / (3600 * ureg.s)\n",
    "v0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Encara que de vegades haurem de forçar la simplificació d'uniotats amb `ito_reduced_units()` (veure https://pint.readthedocs.io/en/0.13/tutorial.html#converting-quantities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "14.0 cubic_centimeter * gram / centimeter ** 3\n"
     ]
    }
   ],
   "source": [
    "density = 1.4 * ureg.gram / ureg.cm**3\n",
    "volume = 10*ureg.cc\n",
    "mass = density*volume\n",
    "print(mass)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "14.0 gram"
      ],
      "text/latex": [
       "$14.0\\ \\mathrm{gram}$"
      ],
      "text/plain": [
       "14.0 <Unit('gram')>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mass.ito_reduced_units()\n",
    "mass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ara que sabem com treballar amb unitats a python ens podrem dedicar a resoldre el nostre problema"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### a) L'energia alliberada en forma de calor per a cada cotxe.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ara ja podem calcular la energia cinética de cada cotxe $Ec=\\frac{1}{2}\\cdot m\\cdot v^{2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "138888.8888888889 kilogram meter<sup>2</sup>/second<sup>2</sup>"
      ],
      "text/latex": [
       "$138888.8888888889\\ \\frac{\\mathrm{kilogram} \\cdot \\mathrm{meter}^{2}}{\\mathrm{second}^{2}}$"
      ],
      "text/plain": [
       "138888.8888888889 <Unit('kilogram * meter ** 2 / second ** 2')>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ec=1/2*m*v0**2\n",
    "Ec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Naturalment l'energia es mesura en J. Podem fer el canvi amb `.ito(ureg.J)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "138888.8888888889 joule"
      ],
      "text/latex": [
       "$138888.8888888889\\ \\mathrm{joule}$"
      ],
      "text/plain": [
       "138888.8888888889 <Unit('joule')>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Ec.ito(ureg.J)\n",
    "Ec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I tenir-la amb un múltiple adient. *pint* ho pot fer amb `.to_compact`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "138.8888888888889 kilojoule\n"
     ]
    }
   ],
   "source": [
    "print (Ec.to_compact())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Que justament és alliberada en forma de calor per a cada cotxe   \n",
    "\n",
    "L'expresió correcta d'aquest resultat seria **Q = 138,8 kJ**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### b) Els temps de frenada si els frens a cada cotxe exerceixen una força constant F = 4 kN   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Com la força de frenada s'oposa a la velocitat tindrà signe negatiu:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-0.004 kilonewton/kilogram"
      ],
      "text/latex": [
       "$-0.004\\ \\frac{\\mathrm{kilonewton}}{\\mathrm{kilogram}}$"
      ],
      "text/plain": [
       "-0.004 <Unit('kilonewton / kilogram')>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F =  -4 * ureg.kN\n",
    "a = F / m\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ho arreglem amb `.ito_base_units()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-4.0 meter/second<sup>2</sup>"
      ],
      "text/latex": [
       "$-4.0\\ \\frac{\\mathrm{meter}}{\\mathrm{second}^{2}}$"
      ],
      "text/plain": [
       "-4.0 <Unit('meter / second ** 2')>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.ito_base_units()\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "4.166666666666667 second"
      ],
      "text/latex": [
       "$4.166666666666667\\ \\mathrm{second}$"
      ],
      "text/plain": [
       "4.166666666666667 <Unit('second')>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = (0 * ureg.m / ureg.s - v0) / a\n",
    "t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per tant tindrem un tems de frenada **t = 4,167 s** "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### c) L'espai recorregut en aquesta frenada   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "34.72222222222223 meter"
      ],
      "text/latex": [
       "$34.72222222222223\\ \\mathrm{meter}$"
      ],
      "text/plain": [
       "34.72222222222223 <Unit('meter')>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = v0 * t + 1 / 2 * a *t**2\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es a dir, l'espai recorregut en aquesta frenada derà de **r = 34,72 m**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### d) Repetiu els apartats anteriors si la velocitat fos el doble (120 km/h) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podem repetir les fòrmules, canviant el valor inicial de v0:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "33.333333333333336 meter/second"
      ],
      "text/latex": [
       "$33.333333333333336\\ \\frac{\\mathrm{meter}}{\\mathrm{second}}$"
      ],
      "text/plain": [
       "33.333333333333336 <Unit('meter / second')>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0 = 120 * ureg.km / ureg.hour\n",
    "v0.ito_base_units()\n",
    "v0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "555.5555555555557 kilojoule\n"
     ]
    }
   ],
   "source": [
    "Ec=1/2*m*v0**2\n",
    "Ec.ito(ureg.J)\n",
    "print (Ec.to_compact())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**a) Q' = 555,6 kJ**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "8.333333333333334 second"
      ],
      "text/latex": [
       "$8.333333333333334\\ \\mathrm{second}$"
      ],
      "text/plain": [
       "8.333333333333334 <Unit('second')>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = (0 * ureg.m / ureg.s - v0) / a\n",
    "t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**b) t' = 8,333 s**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "138.8888888888889 meter"
      ],
      "text/latex": [
       "$138.8888888888889\\ \\mathrm{meter}$"
      ],
      "text/plain": [
       "138.8888888888889 <Unit('meter')>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = v0 * t + 1 / 2 * a *t**2\n",
    "r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**c) r = 138,9 m**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparem resultats:\n",
    "\n",
    "<table>\n",
    "<tbody>\n",
    "<tr><td>v0</td><td>Q</td><td>t</td><td>r</td></tr>\n",
    "<tr><td>60 km/h</td><td>138,8 kJ</td><td>4,167 s</td><td>34,72 m</td></tr>\n",
    "<tr><td>120 km/h</td><td>555,8 kJ</td><td>8,333 s</td><td>138,9 m</td></tr>\n",
    "</tbody>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si bé el temps s'ha duplicat com la velocitat inicial, la calor dissipada i la distància recorreguda s'han multiplicat per 4. Això és degut a la depèndencia quadràtica de **Q** i **r** amb la velocitat inicial. El temps **t**, en canvi, té una dependència linial amb **v0**\n",
    "\n",
    "Veiem gràficament aquestes dependències:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "import numpy as np\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = plt.axes()\n",
    "x = np.linspace(0, 50, 1000)\n",
    "ax.plot(x, 1 / 2 * x * x);\n",
    "plt.title(\"Calor dissipada a cada cotxe\")\n",
    "plt.xlabel(\"v [m/s]\")\n",
    "plt.ylabel(\"Q [kJ]\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes()\n",
    "x = np.linspace(0, 50, 1000)\n",
    "ax.plot(x, x / 4);\n",
    "plt.title(\"Temps de frenada\")\n",
    "plt.xlabel(\"v [m/s]\")\n",
    "plt.ylabel(\"t [s]\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Com imagineu, la gràfica de l'espai recorregut a la frenada és més difícil de fer, ja que depén de **v0** i de **t**, que també depèn de **v0**. Però no per això aquesta dependència **quadràtica** és menys important, com sabreu tots els que estudieu per treure's el carnet de conduir!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$v = v_{0} + a \\cdot t = 0 \\Rightarrow t = - \\frac{v_{0}}{a} $\n",
    "\n",
    "$\\Delta r = v_{0} \\cdot t + \\frac{1}{2}\\cdot a \\cdot t^{2}$\n",
    "\n",
    "$\\Delta r = v_{0} \\cdot (- \\frac{v_{0}}{a}) + \\frac{1}{2}\\cdot a \\cdot {(- \\frac{v_{0}}{a})^{2}}$\n",
    "\n",
    "$\\Delta r = - \\frac{(v_{0})^{2}}{a} + \\frac{1}{2}\\cdot \\frac{(v_{0})^{2}}{a} = \\frac{1}{2} \\frac{(v_{0})^{2}}{a}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BlWqqmLktGVsrS96bGoiDbdM8tdo0qxJCCCOkrVH4vw9P8ss1NR/M7E/7Vg6GLqlWEv5CCNFA4vae5uBP+bwyrhf9vFrfeQUDkmEfIYRoAJ+dzGb9oXM81P9PTLlP/8/gvVcS/kIIcY/SLhWz6OMfuM+rNS/8uaehy7krEv5CCHEPrhSXM2NbMu4tmvH2lL7YWBlHrMqYvxBC1JOqopoZW5PRVGr554z7cGnezNAl3TUJfyGEqIeaGoXHE77n9NVSNj0S3KSmbrgbxvH3iRBCNDEr957m36dyeX5sD4Z2dzd0OXUm4S+EEHW048Ql1h86R0z/jjw8oJOhy6kXCX8hhKiDY+euseTTdAZ1deWFP/doklM33A0JfyGEuEsXClTM2Z5CRxcH1kb3xdpIruy5HeOtXAghGlGJuopHt57AAtj0SDDO9jaGLumeyNU+QghxB1XaGmI/SOVSoZrt0++jo4ujoUu6Z3oN/7i4OFJSUqiurmb27NkkJSVx8uRJHB1vfOGmT5/O0KFD2bVrF1u3bsXS0pJJkyYxceJEfZYlhBB3TVEUXtz1I9+eLSBuYm/u6+xi6JIahN7C/9ixY5w5c4aEhASKiooYN24cISEhvPLKK/j6+urep1arWbduHYmJidjY2BAZGUlYWBgtW7bUV2lCCHHXNh45zz+TfmH2kM48GNTB0OU0GL2Ff3BwML179wbA2dmZ8vJySktLb3lfWloafn5+ODnduEEiKCiI1NRUhg8frq/ShBDiruxOz+GV3ZmM9mvDolE+hi6nQekt/K2srHBwuDGX9c6dOxk8eDCFhYWsXbuW0tJSPDw8WLp0KQUFBbRu/dvUp66uruTn5992m5mZmfWqRaPR1HtdYyU9mz5z6xcat+dTeRoW783B160Zs3rb8dNPpxtlv/9LXz3r/YTv/v37SUxMZNOmTRw7dgxvb2+8vLx45513WLNmDf7+/je9X1GUWq+b/f1wUV1kZmbWe11jJT2bPnPrFxqv5wsFKl5J/A/tWtnzzzkDae1oq/d91uZeek5JSan1Nb1e6nnkyBHeffddNmzYgJOTEyNGjMDLywuAESNG8NNPP+Hh4UFBQYFunby8PNzc3PRZlhBC1KpQVckjm4+jKAqbp/UzaPDrk97Cv6ysjLi4ONavX687eTtnzhyuXLkCQFJSEl27dsXf35/09HRKS0tRqVSkpqYSFBSkr7KEEKJWmiots7Ylc6VEw4apQXi5Gv8lnbXR27DP7t27KSoq4vHHH9ctmzBhAvPnz8fBwQF7e3teffVV7OzseOqpp5g+fToWFhbExsbqTv4KIURjqalReGpHGskXi1gX3ZegTk37MYz3Sm/hP2nSJCZNmnTL8sjIyFuWhYeHEx4erq9ShBDijlbuPc2/0nN4JsKHMb3bGrocvZPpHYQQZm/7sYu65+/OGtzZ0OU0Cgl/IYRZ++Z0Hs9/nsFwH3de/HNPo52ls64k/IUQZivtUjGxH6Ti27YFayb3MepZOuvKfDoVQojfOV+gYtqWE7R2tGXzI8E4NjOveS4l/IUQZievTMPUTUkAbHu0H+4t7AxcUeOT8BdCmJUyTRXTNp+goKySTY8E09mtuaFLMgjz+jtHCGHWKqtrmLM9hdNXy9j4cBABHcx39mA58hdCmIWaGoUFO9P47uw1Vk7ozbDu7oYuyaAk/IUQZmH57kx2pV1hYXh3Jga2N3Q5BifhL4Qwee8d/pmN357nkQGdeGxIF0OX0yRI+AshTNqnJy+zfPdpxvRuy/Nje5jNTVx3IuEvhDBZh7PyeXrnD/Tv3Jp/POiPpaUE/68k/IUQJin1lyLmbE/B2705700Nopm1laFLalIk/IUQJuf01VKmbT6Bm1Mztk3vRws7G0OX1ORI+AshTMov19TEvH8cOxtLtk+/D3cn87t7927ITV5CCJORW6phyvvHqNLWsGN2CB1aOxi6pCZLjvyFECahWF3J1PePU3i9ki3T+tHNQ54I+EfkyF8IYfRUFdVM23KC8wUqtkwLNutpG+6WHPkLIYxaRbWWOdtTSLtUzJroPgzwdjV0SUZBjvyFEEarWlvD3z78niNnCnjtAX9G9Wxj6JKMhhz5CyGMkqIoLPk0nT0/XuX5sT1kvp46kvAXQhgdRVF45V+Z7Ei+zP+FduXR+70MXZLR0euwT1xcHCkpKVRXVzN79mz8/PxYuHAhWq0WNzc3Vq1aha2tLbt27WLr1q1YWloyadIkJk6cqM+yhBBGbvW+LN1EbU+EdTV0OUZJb+F/7Ngxzpw5Q0JCAkVFRYwbN46QkBCio6OJiIggLi6OxMREIiMjWbduHYmJidjY2BAZGUlYWBgtW8rZeiHErdYeOMPab84yuV8HXvizTNRWX3ob9gkODubNN98EwNnZmfLycpKSkggNDQUgNDSUo0ePkpaWhp+fH05OTtjZ2REUFERqaqq+yhJCGLFPfizmtX1ZjO/Tjlci/ST474Hewt/KygoHhxt31+3cuZPBgwdTXl6Ora0tAG5ubuTn51NQUEDr1q1167m6upKfn6+vsoQQRir+2EU2JBcyxq8tcRN7ywyd90jvl3ru37+fxMRENm3axKhRo3TLFUW56ePvl9f22zwzM7NeNWg0mnqva6ykZ9NnTv3uO1PG6//JJ9izGXMC7DiT9ZOhS2o0+vo+6zX8jxw5wrvvvsvGjRtxcnLC3t4ejUaDnZ0dubm5uLu74+HhwcGDB3Xr5OXlERAQcNvt+fr61quOzMzMeq9rrKRn02cu/X7+fTZvHD3HoK6uLLivOX49exi6pEZ1L9/nlJSUWl/T27BPWVkZcXFxrF+/XnfydsCAAezduxeAffv2MWjQIPz9/UlPT6e0tBSVSkVqaipBQUH6KksIYUT2ZFzlyR1p9OvUmvdigrC1kqvTG4rejvx3795NUVERjz/+uG7ZihUrWLp0KQkJCXh6ehIZGYmNjQ1PPfUU06dPx8LCgtjYWJycZEImIczdN6fzmP9hKv7tnXn/kWDsbeVhLA1Jb+E/adIkJk2adMvyzZs337IsPDyc8PBwfZUihDAyh7Pymb09he5tnNg8rR/Nm8lMNA1N/oYSQjQph7PymbktmS5uzYl/9D6c7eUpXPog4S+EaDKOnLkR/J3dmvPPGffRytHW0CWZLAl/IUSTcORMPjO2/hb8rSX49UrCXwhhcBL8jU/CXwhhUN+eKWDG1mS8XB0l+BuRhL8QwmC+PVPA9K0n8HJ15IOZ/SX4G5GEvxDCICT4DUvCXwjR6CT4DU/CXwjRqA6czuVRCX6Dk/AXQjSaPRk5zI5PobuHEx/NkuA3JLlnWgjRKD7/Ppsnd6QR0KElm6cF08JO7tw1JDnyF0Lo3Y4Tl3g84XuCO7Vi26P9JPibADnyF0LoVfzRCzz3+Y8M6urKezFBMjtnEyHhL4TQm41HzvHyvzIJ8/Vg3ZQ+NLOW4G8qag3/Q4cO3dUGhgwZ0mDFCCFMx9oDZ3htXxZj/NryRlQANvIglial1vB/9tlnGTRo0B+ufOTIEb799tsGL0oIYbwURWH1vizWfnOW8X3aETexN9YS/E1OreEfHh7O0qVL/3Dll19+ucELEkIYr5oahb9/eYot/7nA5H4deCXSD0tLC0OXJW6j1vD/NfgvX77MgQMHKCsrQ1EU3evz5s274y8HIYT5qNLWsDDxBz49mc2M+714dowvFhYS/E3VHU/4zpo1i1GjRuHq6toY9QghjJCmSkvsP1P5+nQeT4/qztyhXST4m7g7hr+npyd/+9vfGqMWIYQRKtVUMWNrMicuFLIsshcx/TsauiRxF+4Y/hMmTGDOnDn4+vpiZfXbZVrz5s3Ta2FCiKav4HoFD286zk9Xy3gzqg9/8fc0dEniLt0x/N98800Z9hFC3CK7uJyYjUlcKSlnw9Qghvm4G7okUQd3DP/27dvzxBNPNEYtQggjcTbvOjHvJ3G9opr46fcR3Km1oUsSdXTH8O/YsSMLFiygd+/eNw37TJky5Y4bz8rKYu7cuTzyyCM89NBDLFu2jJMnT+Lo6AjA9OnTGTp0KLt27WLr1q1YWloyadIkJk6ceA8tCSH0Kf1yCQ9vPo6lBSTMCqGHZwtDlyTq4Y7h36pVK1q1akVpaWmdNqxWq1m2bBkhISE3LXvllVfw9fW9adm6detITEzExsaGyMhIwsLCaNmyZZ32J4TQv8NZ+Ty2PYWWDrZsn3EfXq6Ohi5J1FOt4f/cc8+xbNmyPzyx++t7bsfW1pYNGzawYcMG3TKVSnXL+9LS0vDz88PJyQmAoKAgUlNTGT58+F03IYTQv49TLrPo4x/o6uHElmnBeLSwM3RJ4h7UGv779+//w6N9RVFITk6uNfytra2xtr558yqVirVr11JaWoqHhwdLly6loKCA1q1/Gy90dXUlPz+/rn0IIfREURTeOfQzcXt+YkAXF96NCZQpmU1AreH/5ptv3nHlhx56qE47i4qKwtvbGy8vL9555x3WrFmDv7//Te9RFKXWm0MyMzPrtL9faTSaeq9rrKRn09cY/WprFNYfv8YXP5Uy1MuRJ0NakH3+LNl63WvtzO17DPrrudbw79evX4PvbMSIETf9+8UXX2TkyJEcPHhQtzwvL4+AgIDbrv/7cwV1kZmZWe91jZX0bPr03a+mSsvjH33Pnp9KmTW4M4vDfQw+T4+5fY/h3npOSUmp9bVGnWpvzpw5XLlyBYCkpCS6du2Kv78/6enplJaWolKpSE1NJSgoqDHLEkL8jxJ1FTHvJ7Hnx6s8N7YHS0b7Gjz4RcO649U+eXl5uLvX/eaNjIwMVq5cSXZ2NtbW1uzdu5fJkyczf/58HBwcsLe359VXX8XOzo6nnnqK6dOnY2FhQWxsrO7krxCi8WUXl/PIpuNcvKZmzeQ+/Fnu2jVJdwz/J598ku3bt9d5w7169SI+Pv6W5aNHj75lWXh4OOHh4XXehxCiYWVklzB96wnUFVq2PBrMgC5yZ7+pumP4u7m5ERUVhZ+fHzY2v53hX7hwoV4LE0I0rv2ncvm/j07S0t6GnY+F4NNGbt4yZXcM/8GDBzdGHUIIA9r83XmWfXmKnp7OvP9wEO5yDb/Ju2P4jxs3rjHqEEIYgLZGYdl/n7w1socHb0QF4GB7x1gQJkC+y0KYKVVFNfM/PMmB03nMHOTF4ghfrOSKHrMh4S+EGcopKWf6lmR+yi2TB7CYKQl/IczMr1f0qCq0vP9wEEO7yzz85kjCXwgzsvfHqzyR8D0t7W1IlCt6zJqEvxBmQFEU1h44y+p/Z+HfoSUbYgLlih4zJ+EvhIkrr9TydGIaX/6Qw7g+7Xh1vB92NlZ3XlGYNAl/IUzYleJyZsUn8+OVUhZH+DB7cOdaZ80V5kXCXwgTlXKxiNnxKWiqbpzYHe7jYeiSRBMi4S+ECUpMucyST9Jp29KOD2feR1cPmSxR3EzCXwgToq1RWPFVJhuOnGdAFxfWRfellaOtocsSTZCEvxAmolBVyd8+OsmRMwU8HNKRpWN7YGPVqI/sEEZEwl8IE5CRXcLs+BTyr1ewcoIfk4L/ZOiSRBMn4S+EkduZfIlnP8vA1dGWxDkh9G7f0tAlCSMg4S+EkarUKjz7aTr/TPqFgd4uvBXVB5fmzQxdljASEv5CGKGrJRoW7b3C6fwK5gzpwoKR3bCW8X1RBxL+QhiZY+euMe+DVFSaKt6Z0pcIv7aGLkkYITlUEMJIKIrChsPnmLIxiRb2Nrwxpp0Ev6g3OfIXwggUqytZsPMH9mfmEt6zDase6M3l82cNXZYwYhL+QjRxJ38pYt4HJ8kr0/DCn3vwyIBOMj+PuGcS/kI0UYqisOm7C6z4KhOPFnbsnDOAgA5yGadoGHod88/KyiIsLIzt27cDkJOTQ0xMDNHR0fztb3+jsrISgF27djFhwgQeeOABEhMT9VmSEEahRF3F7PgUln15iqHd3fnX/EES/KJB6S381Wo1y5YtIyQkRLfsrbfeIjo6mg8++IB27dqRmJiIWq1m3bp1bNmyhfj4eDZu3EhxcbG+yhKiyUu7VMyYNUc4cDqPpWN8eS8mEGcHG0OXJUyM3sLf1taWDRs24O7+2/NBk5KSCA0NBSA0NJSjR4+SlpaGn58fThDu9hoAABMTSURBVE5O2NnZERQURGpqqr7KEqLJUhSF9789z8R3/4OiwI45IcwYJPPvC/3Q25i/tbU11tY3b768vBxb2xszDLq5uZGfn09BQQGtW7fWvcfV1ZX8/PzbbjMzM7NetWg0mnqva6ykZ+NSVF7NP77LJzm7nP4dHHhyoBv2qqtkZl6tdR1j7re+pOeG06gnfH9/BKMoyk0ff7+8tiMdX1/feu03MzOz3usaK+nZeBz8KY8Fu9Mo01SzLLIXD933p7s62jfWfu+F9Fw3KSkptb7WqDd52dvbo9FoAMjNzcXd3R0PDw8KCgp078nLy8PNza0xyxLCICqqtfz9i1M8svkErs2b8cX8+4np31GGeUSjaNTwHzBgAHv37gVg3759DBo0CH9/f9LT0yktLUWlUpGamkpQUFBjliVEozubV0bkuv+w6bvzPDKgE5/FDqSbPG1LNCK9DftkZGSwcuVKsrOzsba2Zu/evbz22mssXryYhIQEPD09iYyMxMbGhqeeeorp06djYWFBbGwsTk7yP4EwTYqi8MHxX1j25SkcbK15/+EgQn3l2bqi8ekt/Hv16kV8fPwtyzdv3nzLsvDwcMLDw/VVihBNQl6ZhiWfpLM/M49BXV1Z/YA/7i3sDF2WMFNyh68QjeCr9ByWfJqOqlLL0jG+PDrQC0tLGdsXhiPhL4QelaireGFXBp99f4Xe7Z35x4P+eLvLsKYwPAl/IfTkcFY+CxN/IP96BY+HdSV2mLc8UF00GRL+QjQwdWU1r+4+Tfyxi3i7N+e9qYHyXF3R5Ej4C9GATlwo5OmdaVwsVDPjfi8WjOqOnY2VocsS4hYS/kI0gOsV1cTtOc22oxdp38qeD2f2p39nF0OXJUStJPyFuEeHsvJZ8kk6V0rKmTawE0+P6o6DrfyvJZo2+QkVop6K1ZUs+zKTj1Mv08XNkcQ5IQR2bH3nFYVoAiT8haiHPRk5LP3sR4rUlcQO68L84V1lbF8YFQl/Ieogr1TDC7t+5KuMq/Ro24It04Lp1c7Z0GUJUWcS/kLcBW2NwvZjF3lt709UVNfw9KjuzBrcWa7bF0ZLwl+IO0i/XMKzn6Xzw+US7vd2ZVlkL7xcHQ1dlhD3RMJfiFqUaapYvS+LbUcv0NqxGW9N7sOfe7eV+faFSZDwF+J/KIrC7vSrvPTFj+RfryCmf0eeGtkdZ3t5iLowHRL+QvzO+QIVL+76kUNZ+fT0bMGGqUH4d5CpGYTpkfAXght36K45cIZN356nmbUVz4/twdSQjljLCV1hoiT8hVmrqVH49GQ2K/acJr+sgomB7VkY3h13J3nIijBtEv7CbKVdKuaFXT/y/aVi/Du05L2YQPr8qZWhyxKiUUj4C7OTX1bBqr2n2ZF8GdfmzVg1sTcT+raXJ2sJsyLhL8xGeaWW9789x7uHzlFRrWXW4M7MH+6Nk51cxSPMj4S/MHnaGoVPUi+zel8WV0s1jOzhwaIIH7q4NTd0aUIYjIS/MGmHs/JZvjuT01fL8G/vzFuT+9DPS2beFKJRwz8jI4O5c+fSsWNHALp168aMGTNYuHAhWq0WNzc3Vq1aha2tbWOWJUxQZk4py3dncuRMAe1b2fPW5D6M9Wsr4/pC/Fejhr9arWbUqFE8++yzumXPPPMM0dHRREREEBcXR2JiItHR0Y1ZljAhv1xT88b+LD79PpsWdjYsHeNLTEhHmlnLdMtC/F6j3sGiUqluWZaUlERoaCgAoaGhHD16tDFLEibiaomGNUfzGb76IP9Kz2HG/V4cenooMwZ1luAX4jYa/cg/JSWFGTNmUF5ezvz58ykvL9cN87i5uZGfn9+YJQkjd+16BW8f/Jn4Yxepqakhqt+fmD+8Kx4t5CYtIf5Io4a/j48PsbGxhIaGcv78eaZNm0Z1dbXudUVR/nD9zMzMeu1Xo9HUe11jZeo9X6/U8smPJXx6qoRKrUJo5+ZM8HGgo6s1hdnnKcw2dIX6Z+rf49uRnhtOo4Z/ly5d6NKlCwBeXl64urqSk5ODRqPBzs6O3Nxc3N3da13f19e3XvvNzMys97rGylR7LlZXsvm7C2z+7hdKNdWM6d2WJ8K64e3e3GR7ro259QvSc12lpKTU+lqjhn9iYiJqtZqpU6eSn5/PtWvXGD9+PHv37uWvf/0r+/btY9CgQY1ZkjASBdcreP/b88Qfvcj1impG9vDgb2Fd6ekpj1AUoj4aNfxHjBjBggUL2Lt3L5WVlbz44ov4+vqyaNEiEhIS8PT0JDIysjFLEk1cXqmG9YfP8c+ki1RU1zDGry3zhnvj06aFoUsTwqg1avg7OzuzYcOGW5Zv3ry5McsQRuBykZr1h86RkHwJbY3CXwM8iR3mLXflCtFA5A5f0aRkZJfw3uFz/Cs9B0sLmNC3PY8N7UJHF3lmrhANScJfGJyiKBzMymfD4XP85+drNG9mzaMDOzFtoBeeLe0NXZ4QJknCXxhMRbWWXd9fYcORc2TlXqdNCzueifBh8n1/ooXMtCmEXkn4i0aXV6bho+OX2H7sInllFfi0cWL1A/782d8TW2t5bKIQjUHCXzQKRVFI/aWYbUcvsDs9hyqtwqCurrz2gD+DurpiYSETrgnRmCT8hV5pqrTsSrvCtqMXyMguxamZNQ/170hM/450lit3hDAYCX+hF+fyr5Nw4hI7ki9RpK6im0dzXo7sxbg+7XBsJj92Qhia/F8oGkx5pZbd6TkknLjE8QuFWFlaEObrzsMDOhHS2UWGdoRoQiT8xT3LyC7hoxO/8PnJK5RVVNPJxYFF4T5M6NsOd5ldU4gmScJf1EteqYZdaVf4JDWbUzmlNLO2ZLRfWyYFd+A+r9ZylC9EEyfhL+6aqqKavT9e5dOT2Xx3toAaBXq1a8Hf/9qTv/q3w9lBrs0XwlhI+Is/VKWt4duzBXx2Mpt9P+ZSXqWlfSt75g71JrKPJ97uToYuUQhRDxL+4haV1TV893MBX6XnsO9ULsXqKpztbRjftx3j+rQjsGMrGdYRwshJ+AvgxvX4R84U8FVGDv8+lUuZphqnZtaE9fAgolcbhnZ3l7tvhTAhEv5mrEhVyaGsfPZn5nLwp3yuV1TjbG9DeM82jPZrywBvF3n4uRAmSsLfjCiKQlbudb4+ncuBzDxSfymiRgHX5s0Y27sto/3aEtLFBRsrOcIXwtRJ+Ju4kvIqjp27xrdnCjhwOo/s4nLgxlU684Z3JdTHHb92zlhayhi+EOZEwt/EVFRrSb1YzOephZw+8B0/XC6mRgF7GysGersyb7g3w7q708ZZbr4SwpxJ+Bs5TZWWHy6XcOJCIUnnCzl+/hqaqhosLSCgQ0vmDfNmoLcrff7USk7YCiF0JPyNTJGqkuSLRSRfLCT5QhHpl0uo1NYA4O3enKjgPzHQ25VWVQUE+fc0cLVCiKZKwr8JU1VU8+OVUn64XExGdgk/ZJdwLl8FgI2VBb3bt2Ta/Z0I7tiawI6taOVoq1s3M7PQUGULIYyAhH8Tce16BT/llvHT1TLSs0tIv1zC2fzrKMqN19u0sMOvvTMT+rYnuFNrerd3xs5GLsMUQtSPhH8jUhSFYnUV5wpUZP036LNyb/xXcL1S9z7X5s3wb+/MmN5t6d3emV7tnHF3khO0QoiG02TCf/ny5aSlpWFhYcGSJUvo3bu3oUuqF22NQn5ZBZeL1Fy4pubiNdVvHwtUlGqqde91sLWim4cTw33c6ebhRPc2TnTzcMLdqZlMnyCE0KsmEf7Hjx/n4sWLJCQkcPbsWZ555hl27txp6LJuoqnSUqiqpFBVSZH6xse80gpySjRcLS2/8bFEQ15ZBdoaRbeelaUF7VvZ09HFkcg+Leno4kgnFwe6eTjRrqW9XF8vhDCIJhH+R48eJSwsDABvb29KS0u5fv06zZvf+zNes3LLOHjuOpnll6muUdDWKDc+amuorlGoqK6hvFKLqrIadcV/P1ZqUVVUc72immJ1FYWqSsqrtLfdvoOtFW2d7WjrbM9Ab1faOtvRxtkOz5b2eLk40q6VvdwxK4RocppE+BcUFNCz52+XJbq4uJCfn39L+GdmZtZ524/tusyFokogr9b3WFqAvbUldjYW2FtbYm9jgZ21JY42lrR1saKFZ3Oc7axo0cySFnZWtGh2498uDtY42Fj8zxBNDaCGGjXl+dc4m1/nkhuERqOp19fLmJlbz+bWL0jPDalJhL+iKLd8frsxb19f3zpve5eXN8e+P0U3b2+sLC2wsbLEytICa0sLrKwssLWypJm1pcmNsWdmZtbr62XMzK1nc+sXpOe6SklJqfW1JhH+Hh4eFBQU6D7Py8vD1dW1Qbbdws6GDs62dHJ1bJDtCSGEKWgSg9EDBw5k7969AJw6dQp3d/cGGe8XQghxe03iyL9v37707NmTqKgoLCwseOGFFwxdkhBCmLQmEf4ACxYsMHQJQghhNprEsI8QQojGJeEvhBBmSMJfCCHMkIS/EEKYIQvlf++waqL+6GYFIYQQtxcYGHjb5UYT/kIIIRqODPsIIYQZkvAXQggz1GRu8tIHU3lAzN3Iyspi7ty5PPLIIzz00EPk5OSwcOFCtFotbm5urFq1Cltb2ztvyEjExcWRkpJCdXU1s2fPxs/Pz6T7LS8vZ/HixVy7do2Kigrmzp2Lj4+PSff8K41Gw5gxY4iNjSUkJMSke87IyGDu3Ll07NgRgG7dujFjxgy99GyyR/6/f0DMyy+/zLJlywxdkt6o1WqWLVtGSEiIbtlbb71FdHQ0H3zwAe3atSMxMdGAFTasY8eOcebMGRISEti4cSPLly836X4BvvnmG3r16sX27dt54403WLFihcn3/Kt33nmHli1bAqb9cw03/l8eNWoU8fHxxMfH89xzz+mtZ5MN/9oeEGOKbG1t2bBhA+7u7rplSUlJhIaGAhAaGsrRo0cNVV6DCw4O5s033wTA2dmZ8vJyk+4XYPTo0cycOROAnJwcPDw8TL5ngJ9//pmzZ88ydOhQwLR/rgFUKtUty/TVs8mGf0FBAa1atdJ9/usDYkyRtbU1dnY3P+C9vLxc96ehm5ubSfVuZWWFg4MDADt37mTw4MEm3e/vRUVFsWDBApYsWWIWPa9cuZLFixfrPjf1ntVqNSkpKcyYMYMpU6Zw7NgxvfVssmP+d/uAGFP1+15N9Wre/fv3k5iYyKZNmxg1apRuuan2C/DRRx+RmZnJ008/bfLf488++4yAgAA6dOigW2bqPfv4+BAbG0toaCjnz59n2rRpVFdX615vyJ5NNvz1+YAYY2Bvb49Go8HOzo7c3NybhoRMwZEjR3j33XfZuHEjTk5OJt9vRkYGLi4utG3bFl9fX7Rarcn3fPDgQS5dusTBgwe5evUqtra2Jt9zly5d6NKlCwBeXl64urqSk5Ojl55NdtjH3B8QM2DAAF3/+/btY9CgQQauqOGUlZURFxfH+vXrdScCTblfgOTkZDZt2gTcGNJUq9Um3/Mbb7zBxx9/zI4dO3jggQeYO3euyfecmJjItm3bAMjPz+fatWuMHz9eLz2b9B2+r732GsnJyboHxPj4+Bi6JL3IyMhg5cqVZGdnY21tjYeHB6+99hqLFy+moqICT09PXn31VWxsbAxdaoNISEhgzZo1eHl56ZatWLGCpUuXmmS/cONyx2effVZ3FDhv3jx69erFokWLTLbn31uzZg3t2rXj/vvvN+meS0pKWLBgAWq1msrKSubNm4evr69eejbp8BdCCHF7JjvsI4QQonYS/kIIYYYk/IUQwgxJ+AshhBmS8BdCCDMk4S/EXVizZg0jR45k+/btd/X+5ORkVq9efcvyjIwMHnzwQcaPH9/QJQpRJxL+QtylqVOn8tBDD93Ve5OSkggODr5lea9evfjHP/7R0KUJUWcS/kIAkZGRXLlyBYDs7Ow/PDKPiYlh7dq1TJ48mSlTprBz506io6OJiYlBq9UCkJqaSmBgIJ999hkTJ05k8uTJvPTSS43SixB3Q8JfCCAsLIxvvvkGgK+//vqmieJux83NjQ8//BCtVktJSQkffPABWq2WrKwsKisrqaysxNHRkffff581a9bw4Ycf0qtXLzQaTWO0I8QdSfgLAYwcOZIDBw4Adxf+vz4Vzt3dnR49egDg6upKWVkZ33//ve71sWPHEhsby5YtWxgyZMgtU28LYSgS/kJw43F5eXl55OTkUFZWRqdOnf7w/VZWVrf9t6IoHD9+nH79+gEwe/Zs1q5di6IoPPzwwxQVFemlfiHqSsJfiP8aMmQIr7/+uu6pSfWVnJxMYGAgNTU1vP7667i5uTFt2jQCAgJ05xWEMDSTnc9fiLoaOXIkUVFRfPHFF/Xexq/j/b9OH+7o6MikSZNwcnKiQ4cO+Pr6yi8A0STIrJ5C3IU1a9bQqlWru77U849cvnyZ//u//+OTTz5pgMqEqB8Z9hHiLm3btu2ub/KqTUZGBk8++WQDVSRE/cmRvxBCmCE58hdCCDMk4S+EEGZIwl8IIcyQhL8QQpghCX8hhDBDEv5CCGGG/h/uWep8AuOYxAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes()\n",
    "x = np.linspace(0, 50, 1000)\n",
    "ax.plot(x, 1 / 2 * x * x / 4);\n",
    "plt.title(\"Recorregut de frenada\")\n",
    "plt.xlabel(\"v [m/s]\")\n",
    "plt.ylabel(\"r [m]\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Representem la mateixa corba posant la velocitat en $\\frac{km}{h}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes()\n",
    "x = np.linspace(0, 50, 1000)\n",
    "ax.plot(x * 3.6, 1 / 2 * x * x / 4);\n",
    "plt.title(\"Recorregut de frenada\")\n",
    "plt.xlabel(\"v [km/h]\")\n",
    "plt.ylabel(\"r [m]\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Com veieu per a una acceleració de - 4 $\\frac{m}{s}$ es compleix la regla de dividir per 10 i elevar al quadrat la velocitat en $\\frac{km}{h}$ per obtenir la distància de seguretat en $m$. Aquesta acceleració correspon a **0,4g** , valor raonable en un cas real."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}