From 1caa1cc4db95746d5499fa025cb554419c7f5a9a Mon Sep 17 00:00:00 2001 From: Your Name Date: Fri, 23 Mar 2018 06:51:12 -0400 Subject: [PATCH] Examen1 --- exams/Examen-01_2018_1_1032478036.ipynb | 286 ++++++++++++++++++++++++ 1 file changed, 286 insertions(+) create mode 100644 exams/Examen-01_2018_1_1032478036.ipynb diff --git a/exams/Examen-01_2018_1_1032478036.ipynb b/exams/Examen-01_2018_1_1032478036.ipynb new file mode 100644 index 0000000..11ef490 --- /dev/null +++ b/exams/Examen-01_2018_1_1032478036.ipynb @@ -0,0 +1,286 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Primer Examen 10%\n", + "Un vehículo parte del reposo en un punto con una aceleración constante de $a_1$. 10 segundos después pasa por el mismo punto, y en la misma dirección, un segundo vehículo con una rapidez de 10 m/s y con aceleración constante $a_2$. Calcule el punto de encuentro: \n", + "1. Gráficamente \n", + "1. Encontrando las raíces del polinomio generado a partir de igualar las dos ecuaciones de movimiento.\n", + "1. Grafique el polinomio generado\n", + "\n", + "_Ayuda:_\n", + "La ecuación de movimiento para el movimiento uniformemente acelerado es:\n", + "\\begin{align}\n", + "x=x_0+v_0 (t-t_0)+\\tfrac{1}{2} a (t-t_0)^2\\,,\n", + "\\end{align}\n", + "donde\n", + "* $x_0$ es la posición inicial\n", + "* $v_0$ es la rapidez inicial\n", + "* $t_0$ es el tiempo inicial\n", + "\n", + "Ejecute la siguiente celda para fijar los valores de las aceleraciones en su caso" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n", + "a1=3 m/s² and a2=7 m/s²\n" + ] + } + ], + "source": [ + "%pylab inline\n", + "import numpy as np\n", + "a1=np.random.choice([2,3,4])\n", + "a2=a1+4\n", + "print('a1={} m/s² and a2={} m/s²'.format(a1,a2))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy import optimize" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Se definen las ecuaciones de movimiento para cada vehiculo, teniendo en cuenta los valores de aceleracion, velocidad y timepo para cada caso" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "t=np.linspace(0,30,50)\n", + "t2=np.linspace(10,30,50)\n", + "a1=3. #aceleracion vehiculo 1\n", + "a2=7. #aceleracion vehiculo 2\n", + "x0=0. #posicion inicial vehiculo 1 y del vehiculo 2 despues de 10s. Este corresponde al origen del sistema de coordenadas\n", + "v0=10. #velocidad inicial del vehiculo 2\n", + "t0=10. #tiempo inicial vehiculo 2\n", + "\n", + "#Ecuacion de movimiento vehiculo 1\n", + "def x1(t):\n", + " return x0+0.5*a1*t**2\n", + "\n", + "#Ecuacion de movimiento vehiculo 2\n", + "def x2(t):\n", + " return x0+v0*(t-t0)+0.5*a2*(t-t0)**2\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Graficamente" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEKCAYAAAAFJbKyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nt2jiUEop5RZNHEoppdzy/6Q1XrEG1hNqAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(t,x1(t), linewidth=3, label=\"vehiculo 1\")\n", + "plt.plot(t2,x2(t2), linewidth=3, label=\"vehiculo 2\")\n", + "plt.legend()\n", + "plt.xlabel(\"Tiempo[s]\")\n", + "plt.ylabel(\"Posicion[m]\")\n", + "plt.grid()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "De esta manera, graficamente el punto de encuentro se dara aproximadamente pasados 25 segundos y ambos tendran una posicion aproximada de 1km " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Raices del polinomio" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Se define el polinomio que resulta de igualar las dos ecuaciones de movimiento antes descritas" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def X(t):\n", + " return x1(t)-x2(t)\n", + "tcomun=optimize.newton(X,20.) #Encuentra la raiz utilizando el metodo de Newton " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "El tiempo al que estaran en la misma posicion es t=25.000000000000004 s\n", + "Los vehiculos se encuentran en x=937.5000000000003 m\n" + ] + } + ], + "source": [ + "print('El tiempo al que estaran en la misma posicion es t={} s'.format(tcomun))\n", + "print('Los vehiculos se encuentran en x={} m'.format(x1(tcomun)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Evalua el tiempo encontrado en cada ecuacion de movimiento y verifica que en ese tiempo, ambos vehiculos tienen la misma posicion:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(937.5000000000003, 937.5000000000005)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x1(tcomun),x2(tcomun) " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Grafica del polinomio" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEKCAYAAAAfGVI8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJMypEIiIhDkVAhGRMKdCICIS5v4fgBL5N3oKX/QAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "tc=np.linspace(10,30,50)\n", + "plt.plot(tc,X(tc), linewidth=3, color=\"green\")\n", + "plt.xlabel(\"Tiempo[s]\")\n", + "plt.grid()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Se grafica el polinomio resultante y se verifica que su raiz esta en 25" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "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": "3.4.2" + }, + "toc": { + "colors": { + "hover_highlight": "#DAA520", + "running_highlight": "#FF0000", + "selected_highlight": "#FFD700" + }, + "moveMenuLeft": true, + "nav_menu": { + "height": "30px", + "width": "252px" + }, + "navigate_menu": true, + "number_sections": true, + "sideBar": true, + "threshold": 4, + "toc_cell": false, + "toc_section_display": "block", + "toc_window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}