Distance, Velocity and Acceleration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distance, Velocity and Acceleration\n",
    "\n",
    "### Acceleration events\n",
    "\n",
    "This Jupyter notebook shows the effects of acceleration on the position of an object. If you were driving a car, you can accelerate by stepping on the gas pedal and deccelerate by stepping on the brakes. You can change the values in the cell below to create a sequence of accelerations, with a corresponding sequence of durations for these accelerations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "accels = [ 0.5, -0.5, 0, -1, 1, 0 ]\n",
    "durations = [ 15, 15, 20, 10, 10, 20 ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Graphs\n",
    "\n",
    "Running the cell below will generate a graph of both the position of your accelerating/deccelerating object and its corresponding velocity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
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       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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WcefmPoH8uHAvW5YfIqh9Par4eTg6LOXESpRURWQe5N9e84uIFLaoviqnRITn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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107d6b7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "last_v = 0\n",
    "last_d = 0\n",
    "last_time = 0\n",
    "\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation, rc\n",
    "from IPython.display import HTML\n",
    "\n",
    "f, (ax1, ax2, ax3) = plt.subplots(3, sharex=True)\n",
    "f.set_dpi(100)\n",
    "f.set_figwidth(5)\n",
    "f.set_figheight(5)\n",
    "\n",
    "ax1.set_ylabel(\"position (m)\")\n",
    "ax2.set_ylabel(\"velocity (m/s)\")\n",
    "ax3.set_ylabel(\"acceleration (m/s^2)\")\n",
    "ax3.set_xlabel(\"time (s)\")\n",
    "\n",
    "timesteps = np.array([])\n",
    "positions = np.array([])\n",
    "velocities = np.array([])\n",
    "accelerations = np.array([])\n",
    "\n",
    "for i in range(len(accels)):\n",
    "    slice = np.linspace(0, durations[i], durations[i] + 1)\n",
    "    ys = 0.5 * accels[i] * np.square(slice) + last_v * slice + last_d\n",
    "    vs = accels[i] * slice + last_v\n",
    "    ts = slice + last_time\n",
    "    accs = [accels[i]] * (durations[i] + 1)\n",
    "    last_v = vs[len(vs) - 1]\n",
    "    last_d = ys[len(ys) - 1]\n",
    "    last_time = sum(durations[:i + 1])\n",
    "    timesteps = np.append(timesteps, ts)\n",
    "    positions = np.append(positions, ys)\n",
    "    velocities = np.append(velocities, vs)\n",
    "    accelerations = np.append(accelerations, accs)\n",
    "    if (ys[0] < ys[len(ys) - 1]):\n",
    "        ypos = ys[len(ys) / 4] - 5\n",
    "    else:\n",
    "        ypos = ys[len(ys) / 4] + 5\n",
    "    ax1.text(ts[len(ts) / 4], ypos, str(accels[i]) + \" m/s^2\", fontsize=8)\n",
    "    if (vs[0] < vs[len(vs) - 1]):\n",
    "        ypos = vs[len(vs) / 4] - 1\n",
    "    else:\n",
    "        ypos = vs[len(vs) / 4] + 1\n",
    "    ax2.text(ts[len(ts) / 4], ypos, str(durations[i]) + \" sec\", fontsize=8)\n",
    "    ax1.plot(ts, ys)\n",
    "    ax2.plot(ts, vs)\n",
    "    ax3.plot(ts, accs)\n",
    "\n",
    "def expand_range(ax, data):\n",
    "    min_val = min(data)\n",
    "    max_val = max(data)\n",
    "    mid = (max_val + min_val) / 2\n",
    "    expansion = ((max_val - min_val) * 1.5) / 2\n",
    "    ax.set_ylim((mid - expansion, mid + expansion))\n",
    "\n",
    "expand_range(ax1, positions)\n",
    "expand_range(ax2, velocities)\n",
    "expand_range(ax3, accelerations)\n",
    "\n",
    "position_marker, = ax1.plot(timesteps[0], positions[0], marker='o')\n",
    "velocity_marker, = ax2.plot(timesteps[0], velocities[0], marker='o')\n",
    "acceleration_marker, = ax3.plot(timesteps[0], accelerations[0], marker='o')\n",
    "\n",
    "def animate(i):\n",
    "    position_marker.set_data(timesteps[i], positions[i])\n",
    "    velocity_marker.set_data(timesteps[i], velocities[i])\n",
    "    acceleration_marker.set_data(timesteps[i], accelerations[i])\n",
    "    return (position_marker, velocity_marker, acceleration_marker, )\n",
    "\n",
    "anim = animation.FuncAnimation(f, animate, frames=len(timesteps), interval=100, blit=True)\n",
    "\n",
    "import matplotlib.animation as animation\n",
    "\n",
    "if u'ffmpeg' in animation.writers.list():\n",
    "    HTML(anim.to_html5_video())    ### doesn't work without ffmpeg\n",
    "else:\n",
    "    filename = \"acceleration.mp4\"\n",
    "    anim.save(filename, writer='avconv')\n",
    "    import ipywidgets as widgets\n",
    "    from IPython.display import display\n",
    "    html = widgets.HTML(\"Your animation is ready for download: <a href='./\" + filename + \"' download>\" + filename + \"</a>\")\n",
    "    display(html)\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}