Vaja_1.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Vaja 1.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPyu8f3pV9OiUbw2AA+iOHT",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/mihakodric/Dinamika/blob/main/Vaja_1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Vaja 1: Kinematika točke\n",
        "\n",
        "## Premočrno gibanje\n",
        "$x(t)$\n",
        "\n",
        "## Kartezijev koordinatni sistem\n",
        "$x(t)$ in $y(t)$"
      ],
      "metadata": {
        "id": "Sq66r0MBDYoH"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Naloga 1\n",
        "Točka se pomika vzdolž $x$ osi z začetno hitrostjo $v_{x}=50$ m/s (pri času $t=0$ s). V prvih štirih sekundah ne pospešuje, nato pa nanju deluje zavirajoča sil, ki zagotovi konstanten pojemek $a_{x}=-10$ m/s$^{2}$.\n",
        "- Narišite hitrostni profil točke.\n",
        "- Izračunajte hitrost $v_{x}$ in $x$ koordinato točke pri $t_{1}=8$ s in $t_{2}=12$ s.\n",
        "- Poiščite največjo pozitivno $x$ koordinato, ki jo v tem času doseže točka. Določite tudi celotno pot, ki jo je točka opravila."
      ],
      "metadata": {
        "id": "P7ecNkZAV1dA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "t2S4fLz9DXpd"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "vx_0 = 50\n",
        "ax_0 = 0\n",
        "ax_1 = -10\n",
        "\n",
        "mejni_časi = [0, 4, 12];\n",
        "časovni_korak = 0.01\n",
        "čas = np.concatenate([np.arange(mejni_časi[0], mejni_časi[1], časovni_korak), \n",
        "                      np.arange(mejni_časi[1], mejni_časi[2], časovni_korak)])\n",
        "\n",
        "def pomik_x(t):\n",
        "  if mejni_časi[0] <= t < mejni_časi[1]:\n",
        "    x = 50*t\n",
        "  else:\n",
        "    x = -10*t**2/2+90*t-80\n",
        "  return x\n",
        "\n",
        "def hitrost_x(t):\n",
        "  if mejni_časi[0] <= t < mejni_časi[1]:\n",
        "    v = vx_0\n",
        "  else:\n",
        "    v = -10*t + 90\n",
        "  return v\n",
        "\n",
        "def pospešek_x(t):\n",
        "  if mejni_časi[0] <= t < mejni_časi[1]:\n",
        "    a = ax_0\n",
        "  else:\n",
        "    a = ax_1\n",
        "  return a\n",
        "\n",
        "pomik = []\n",
        "hitrost = []\n",
        "pospešek = []\n",
        "for t in čas:\n",
        "  pomik.append(pomik_x(t))\n",
        "  hitrost.append(hitrost_x(t))\n",
        "  pospešek.append(pospešek_x(t))\n"
      ],
      "metadata": {
        "id": "25DaTcCYXBxz"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "# ax.plot(čas, pomik, label = \"Pomik [m]\")\n",
        "ax.plot(čas, hitrost, label = \"Hitrost [m/s]\")\n",
        "ax.plot(čas, pospešek, label = \"Pospešek [m/s$^2$]\")\n",
        "ax.grid()\n",
        "ax.legend()\n",
        "plt.xlabel(\"t [s]\")"
      ],
      "metadata": {
        "id": "rxa_vhpaDpsz",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "9998c8e7-3a27-406d-b20a-fdd671aedc43"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 0, 't [s]')"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "t = [8, 12]\n",
        "print(\"x(t): \", [pomik_x(_) for _ in t])\n",
        "print(\"v(t): \", [hitrost_x(_) for _ in t])\n",
        "print(\"a(t): \", [pospešek_x(_) for _ in t])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_OwCA-hagvcr",
        "outputId": "72827a86-0404-428b-eda8-81ae107a2d38"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x(t):  [320.0, 280.0]\n",
            "v(t):  [10, -30]\n",
            "a(t):  [-10, -10]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.plot(čas, pomik, label = \"Pomik [m]\")\n",
        "ax.plot(čas, hitrost, label = \"Hitrost [m/s]\")\n",
        "ax.plot(čas, pospešek, label = \"Pospešek [m/s$^2$]\")\n",
        "ax.set_yticks([pomik_x(0), pomik_x(9), pomik_x(12)])\n",
        "ax.set_xticks([0, 4, 9, 12])\n",
        "ax.grid()\n",
        "ax.legend()\n",
        "ax.axvline(9, c=\"k\")\n",
        "plt.xlabel(\"t [s]\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "mmXsAHVqhlho",
        "outputId": "03e20619-dbee-4dea-c57f-b257e34404b1"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 0, 't [s]')"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RpKSk0KJFCzp16sSTTz5JUFDQ+eGKAaZPn86+fftwd3cnPz+/oV8ih1ZWbuGzpCz+8cMeThSVcFdsOP9zQzdCZLwXh9Q6wJO/392byde257Wlu/jrkh18tukAr4zqydWdgpu8HtsI9xqusM9Yccjfi0eFTExM5OLpAC/nXCeipKQkEhISaNmyJWDM6PTTTz/xl7/8hYyMDH7/+98zcuRIbrjhhiuq8dwvm+joaHr27EmrVq0A6NixI1lZWQQFBbFixQrmzJkDQK9evRg7diy33XZbtePLi7r59cAJnv86jR2HC+nfoQV/uTmSqDbN64aaMEfP1v7MmxLPyp3HeOXb7dz30UZu7tWKF0ZGEubfdL/4pTHQSry9a+7NFhgYyNatW0lISGDmzJlMnTr1is5Tecjfi4cDLisro6ioiPz8/PNt+N999x2PPfYYmzdvJi4uToYJrqeCM6W8sDiVO95fR+7ps8y4ry8LHxwgwS6qUEpxfWQoK58azBPDuvD9jqMM/ftqZq7ZS0mZpfYDNIJaw10pFaGUWqWU2qGU2q6UeqJifYxSaoNSaotSKrliSj2U4R2lVLpSaptSqq+1Pwmz+fr6cvLkyWq3xcfHs2bNGnJycigvL+ezzz5j8ODB5OTkYLFYuPPOO5k2bRqbN2+u9VhXYtWqVQwZMgQAi8VCVlYWQ4YM4fXXX6egoKDGCbrFBVprFv96kGF/X82CjQeYdHUHVj41mJG9WsmAXuKyPFydefL6rqx8cjBXdwpi+rJd3PKvtfx64ITVz12XZpky4I9a681KKV8gRSn1A/AG8IrWeplS6qaKjxOAEUCXiqU/8H7Fv3Zr4sSJPPzww+dvglbWqlUrpk+fzpAhQ87fUB01ahRbt25l0qRJWCzGb/HXXnut2mPVdEO1LpYtW8bo0aMB48mdcePGUVBQgNaaxx9/nIAA2+hKbaasvCKe/Wobv6Tn0jvcn8RJ8XKlLuqlbZAXH98fxw87jvLif9K44/113H9Ve/7nxm7WO6nWul4L8B+MSbJXAGMq1t0LLKj4/wfAvZX23w20qumYsbGx+mI7duy4ZF11CgsL67SfPRg8eLBOSkqq12v69OmjS0pKat1v1apVeuTIkVda2iVqel/q+t6arbzcoj9Zt0/3+Msy3fPF5Xruun26rNxidlnN2uDBg3Xv3r3NLqNZKzxTol9cnKrbP7tEX/XqSv325z9c8bGAZH2ZXK3XDVWlVHuM+VQ3An8AViil3sRo3rm6Yrc2QOWhDLMr1h2+6FgPAg8ChIaGVhnnHMDf379OzRPl5eWN2ozRnPn5+TFhwgReeuklbrrppjq9Zs2aNRQXF1NcXHzZfb788kumT59OTExMo30ta3pfiouLL3m/m5tjRRZmpZ5l9wkLUUHOTIpyJehsJj//lGl2ac1afn4+5eXlzf79NdsQf4iI92DO9rNk5lms8vVSRvjXYUelfIA1wP9prb9SSr0DrNFaf6mUuht4UGt9nVJqCTBda7224nX/BZ7RWl/2MZN+/frpi59C2blzJz169Ki1LmtOkC2uXE3vS13fWzNYLJp5G/YzfdkuXJwUL9zcg7v7RUi7eh0lJCSQn59fr/kHHFlJmYW1P69haMV9sfpSSqVorat9brpOV+5KKVfgS2C+1vqritX3A09U/P8L4OOK/x8EIiq9PLxinRDN2pGCYp76fAvr9uYyqGtLpt8RLVPaCatyc3HCyUoXDrWGuzIuWWYBO7XWb1XadAgYDKwGhgK/Vaz/BvidUmohxo3UAq11lSYZIZqb5WmHeebLVErKLLx2RzT3xMnVurBtdblyvwYYD6Qqpc79rfVn4AHgbaWUC1BMRfs5sBS4CUgHioBJjVqxEI2oqKSMv367g4VJWUS38efte2Lo2NJ+JkkWjqvWcK9oO7/cJcwlk3RW3MF9rIF1CWF1qdkFPLHwV/blnuaRhE48eV1X3FykX5+wD7Yx/IAQjUhrTeK6TF5dupMgb3fmT+1vytgfQliTXKY0Q0uXLqWwsJBvv/22WfcgXbx4MQ888ABjxozh+++/N7ucOjlZXMpjCzbzyrc7GNw1hOV/GCjBLuyShHstnJ2diYmJISoqirvuuouiIusPxt+7d2/uvvtu0tLSLpkw5GKZmZlERUXVuo+np2eVES7rqqZJPm677TY++ugjZs6cyaJFi4ALI2kGBQWRk5NT7/NZ045Dhdzyr7Ws2H6U50Z056MJsQR4uZldlhBWIeFei3MjQ6alpeHm5sbMmTOtfs42bdqwfPlynnvuuUY7ZqdOna7o2eMNGzYwYMCAGveZNm0ajz1m3GY59/U6Nzplc/F5Uha3v/cLRSXlfPbAAB4a3EmehhF2TcK9HgYOHEh6ejoAb731FlFRUURFRfHPf/4TgNOnTzNy5Eh69+5NVFQUixYtIjMzk+7duzN27Fh69OjB6NGjz1/9f/rpp8THxxMTE8NDDz1EeXl5tcc4p7r9K8vIyKBPnz4kJSXV+Hmcq2nixIl07dqVsWPHsnLlSq655hq6dOnCpk2bgKqTfFRXl9aaZ555hhEjRtC3b/McH664tJynv9jKn77cRr/2gSx9YiDxHZr3rPVCNAa5oVpHZWVl5ye9SElJYc6cOWzcuBGtNf3792fw4MFkZGTQunVrvvvuOwAKCgo4ceIEu3fvZtasWVxzzTVMnjyZ9957j5EjR7Jo0SJ++eUXXF1defTRR5k/fz7e3t6XHAOMoK1u/0GDBgGwe/du7rnnHhITE+ndu3etn096ejpffPEFs2fPJi4ujgULFrB27Vq++eYbXn31VRYvXlxlko/ly5dfUte//vUvVq5cSUFBAenp6VWmHmwOjhQU89C8ZLZmF/D7oZ35w3VdcZY5TIWDsIlwf33T6+zK21XttvrOUXpO9xbdeSb+mVr3qzwb08CBA5kyZQrvv/8+t99++/kx2++44w5+/vlnhg8fzh//+EeeeeYZbr75ZgYOHMiJEyeIiIjgmmuuAWDcuHG88847eHh4kJKSQlxc3PnzhISEcN99911yDID//ve/1e4/aNAgjh8/zqhRo/jqq6+IjIys0+ffoUMHoqOjAejZsyfDhg1DKUV0dDSZmZkAVSb5iI6OvqSuxx9/nMcff7xO52tqKftP8PCnKRSdLeOD8bHc2DPM7JKEaFI2Ee5mung2ppp07dqVzZs3s3TpUl544QWGDRvGhAkTLmnbVUqhteb+++8/P9RvZRcf48UXX7zs/pmZmfj7+9O2bVvWrl1b53C/eGKPypN+VDfJR3Wf24svvlinczW1z5OzeOHrNML8Pfh0Sn+6hcnYQ8Lx2ES413SFbcbAYQMHDmTixIk8++yzaK35+uuvmTdvHocOHaJFixaMGzeOgIAAPv74YyZMmMCBAwdYv349V111FQsWLODaa69l2LBhjBo1iieffJKQkBDy8vI4efIkrq6ulxwDuOz+YMyj+vXXX3PjjTfi4+PDfffd1+DPsfIkH0C1n1tzU1ZuYdp3O0lcl8m1nYN5974+8jSMcFg2Ee7NTd++fZk4cSLx8fEATJ06lT59+rBixQqefvppnJyccHV15f333wegW7duzJgxg8mTJxMZGckjjzyCl5cX06ZN44YbbsBiseDq6sqMGTMoKCio9hiRkZHV7h8WZjQ3eHt7s2TJEq6//np8fHwumci7vipP8gGQmppabV3NRcGZUh6bv5m16TlMubYDz43ojotJs84L0SxcbqD3plzsebKOffv26Z49e9pcDXWd5ONy2rZtq48fP17ttsaerONA7ml93d9X685//k5/nnSgUY8t6kcm66i/VatWXfFrqWGyDrm0cQDOzs4UFBTUqxPT5s2bcXV1rfe5zt2ALi0txcnJ+t9eW7Pyuf29dRwtLGbu5P7c1S+i9hcJ4QCkWcbK2rdvT1pamqk1REREkJWVVfuOjeDcDeimuBeyYvsRnlj4Ky193Vn4YH86h8iNUyHOkXAXNkdrzay1+/i/pTvpHR7Ax/f3I9jHvfYXCuFAJNyFTbFYNH9dsoPEdZmMiArjrbtj8HSrfz8HIeydhLuwGSVlFv74xVa+3XqIKdd24PmbeuAkPU6FqFazDnettQzuZGd0HSdkv9jps2U8/GkKP/+Ww3MjuvPQ4E6NXJkQ9qXZhruHhwe5ubkEBQVJwNsJrTW5ubl4eHjU63V5p0uYlJhEanY+b4zuxd3yRIwQtWq24R4eHk52djbHjx+vcb/i4uJ6h4Wwvsu9Lx4eHoSHh9f5OAfzzzB+1kYOnjjDB+P7cX1kaGOWKYTdarbh7urqSocOHWrdb/Xq1fTp06cJKhL10RjvS/qxk4yftYlTZ8uYN6W/DNUrRD0023AXjm3HoULGzdqIs5Pi84euokcrP7NLEsKmSLiLZmdrVj4TZm/C282Z+Q8MoEOwt9klCWFzJNxFs5KcmcekOUkEeLuyYOoAIlp4mV2SEDZJwl00G+v25jD1k2TC/DyY/0B/Wvl7ml2SEDZLBg4TzcLq3ceYNCeJ8EBPFj40QIJdiAaSK3dhupU7jvLo/M10DvHh06n9aeEtE2wI0VAS7sJUP+46yiPzU4hs5cfcyf3x96r/MMNCiEtJuAvTrNlznIfnbaZ7mB9zp/TH31OCXYjGIm3uwhRrf8vhgbnJdA7xYd6UeAl2IRqZhLtocuv25jB1bhIdg72ZP7W/TGIthBVIuIsmtTEjlymJybRt4cX8qf0JlJunQliFhLtoMin785iUmETrAA/mTx1AkMyeJITVSLiLJrHzcCET5yQR6ufBZw8MoKWvBLsQ1iThLqwuK6+I+2dvwtvNhXlT4gnxkyGahbA2eRRSWFXOqbOMn7WRs2UWvnj4KsIDZawYIZqCXLkLqzlZXMrEOZs4UljM7IlxdA31NbskIRyGXLkLqyi1aB6al8LOwyf5eEI/YtsFml2SEA5Fwl00unKL5oOtZ0k+WsRbd/dmSPcQs0sSwuFIs4xoVFprXvxPGslHy3lhZA/u6Fv3+VKFEI1Hwl00qn+u/I35Gw9wUwdXpg7saHY5QjgsaZYRjWbu+kze/u9v3N0vnBFBeWaXI4RDkyt30SiWbDvES99s57oeobx6ezRKKbNLEsKhSbiLBlv7Ww5PLtpCv3aBvHtfH1yc5dtKCLPJT6FokK1Z+Tw4L5lOLX34+P44PFydzS5JCIGEu2iAvcdPMSkxiRbebsydLGOyC9GcSLiLK3KkoJgJszahgHlT+st4MUI0M/K0jKi3/KISJszeSMGZUhY+OIAOwd5mlySEuIhcuYt6OVNSzpRPksnMKeLD8bFEtfE3uyQhRDXkyl3UWWm5hccWbGbzgRPMuK8vV3cONrskIcRlyJW7qBOLRfPMl9v4cdcx/ndUFDdFtzK7JCFEDSTcRZ1MX76LrzYf5MnrujJuQDuzyxFC1ELCXdTqgzV7+fCnDCZc1Y7Hh3U2uxwhRB1IuIsafZGcxWvLdnFzr1a8fEtPGVZACBsh4S4ua+WOozz7VSrXdg7m73f3xslJgl0IWyHhLqqVlJnHYws207O1HzPHx+LuIsMKCGFLJNzFJXYdKWRKYhJtAjyZMzEOH3d5YlYIWyPhLqrIyivi/tmb8HRzZu6UeIJ83M0uSQhxBSTcxXk5p84yYfYmzpSUM3dyf8IDvcwuSQhxheTvbQHAqbNlTJqTxOGCM3w6pT/dwnzNLkkI0QAS7oKzZeU8NC+ZHYcL+WhCLP3atzC7JCFEA0mzjIMrt2ieWrSVX9JzeePOXgztHmp2SUKIRiDh7sC01rz8zXa+Sz3M8zf14M7YcLNLEkI0Egl3B/bOf9OZt2E/Dw3uyAODOppdjhCiEUm4O6h5G/bzj5V7GB0bzrPDu5tdjhCikUm4O6Dvth3mxf+kMax7CNPviJbxYoSwQxLuDuaX9ByeXLSFfu0Cefe+vrg4y7eAEPZIfrIdSGp2AQ/OTaZDsDcfT4jD003GixHCXkm4O4h9OaeZOGcTAV5uzJ0Sj7+Xq9klCSGsSMLdARwtLGb8rI0AzJsST6ifh8kVCSGsTcLdzhUUlTJh1iZOnC4hcVI8HVv6mF2SEKIJyPADdqy4tJypc5PYl3OaOZPiiA73N7skIUQTkXC3U2XlFn63YCpg3DQAABRUSURBVDPJ+0/w7r19uaZzsNklCSGakDTL2CGtNc9+lcrKncf466goRvZqZXZJQogmJuFuh6Yv38W/U7L5w3VdGD+gndnlCCFMIOFuZz76KYMP1mQwfkA7nhjWxexyhBAmkXC3I1+mZPN/S3cyMroVL9/aU4YVEMKBSbjbiR93HeVPX27jms5BvDWmN85OEuxCODIJdzuQsj+PR+dvJrKVHx+M74e7iwwrIISjk3C3cbuPnGTSnCRa+XuSOCkOH3d5ulUIIeFu07JPFDFh9kY8XJ2ZOzmeIB93s0sSQjQTEu42KvfUWSbM2sSZknLmToknooWX2SUJIZoR+RveBp06W8akxCQO5p/h06n96R7mZ3ZJQohmRsLdxpSUWXh4XgrbDxXywbhY4tq3MLskIUQzJM0yNsRi0Tz1+RbWpufw+p29uC4y1OyShBDNlIS7jdBa88q321my7TDPjejO6Nhws0sSQjRjEu424l8/pvPJ+v08OKgjDw3uZHY5QohmTsLdBszfuJ+3ftjDnX3DeXZ4d7PLEULYAAn3Zm5p6mFeWJzG0O4hTL8zGicZVkAIUQcS7s3YuvQc/rBwC33bBjLjvr64OsvbJYSoG0mLZirtYAEPzkuhQ7A3s++Pw9NNxosRQtSdhHsztC/nNPfP3oS/pyufTI7H38vV7JKEEDZGwr2ZOVZYzPhZG9HA3CnxhPl7mF2SEMIGSbg3IwVnSpkwexMnTpeQOCmOTi19zC5JCGGjZPiBZqK4tJwHPklm7/FTzJkYT6/wALNLEkLYMAn3ZqCs3MLvFvxK0v48/nVvH67tEmx2SUIIGyfNMibTWvPnr1NZufMof721Jzf3am12SUIIOyDhbrI3Vuzm8+RsHh/WhfFXtTe7HCGEnZBwN9HHP2fw/uq9jO3fliev62J2OUIIOyLhbpKvf81m2nc7uSk6jL+OikIpGVZACNF4JNxNsGrXMZ7+YhtXdwriH2NicJbxYoQQjUzCvYml7D/BI/NT6N7Klw/Gx+LuIsMKCCEan4R7E9pz9CSTE5MI8/MgcVI8vh4yrIAQwjok3JvIwfwzTJi1CTcXJ+ZN6U+wj7vZJQkh7JiEexPIO13ChFkbOV1SxtzJ8US08DK7JCGEnZNwt7LTZ8uYlJhE9okzzLo/jh6t/MwuSQjhAGT4ASsqKbPw8KcppB0sYOa4WOI7tDC7JCGEg5ArdyuxWDT/88VWfv4th9fuiOb6yFCzSxJCOBAJdyvQWvPXJTv4Zushnh3Rnbv7RZhdkhDCwUi4W8GMVekkrstk6rUdeGhQR7PLEUI4IAn3RvbZpgO8+f0e7ujThj/f1EOGFRBCmELCvREtTzvM81+nMqRbS14f3QsnGVZACGESCfdGsn5vLo9/toWYiADeGxuLq7N8aYUQ5pEEagRpBwt4YG4y7YK8mD0xDk83GS9GCGEuCfcGysw5zcQ5m/D3dGXulHgCvNzMLkkIISTcG+LYyWImzN5EuUXzyeR4Wvl7ml2SEEIA0kP1ihUWl3L/7CRyTp1lwQMD6BziY3ZJQghxnly5X4Hi0nKmfpJM+rGTfDA+lpiIALNLEkKIKuTKvZ7Kyi08/tmvJGXm8fY9fRjYpaXZJQkhxCXkyr0etNa8sDiN73cc5aWbI7m1d2uzSxJCiGpJuNfDm9/vZmFSFo8P7czEazqYXY4QQlyWhHsdzV67jxmr9nJvfFuevL6r2eUIIUSNbLvNvSCblsfWQlpe9dtrHdelhu2VXrtpXx6bfsnkuXYBTO1Witq5r5bD1nTeup2zcV9by3GtUK9fQTqU9gdXeTxUCDPYdrhnJ9Fzx99gh3VPEw/EuwFHgS+sey570Rdg6wsQGgXhccYSEQeBHerwS0wI0VC2He6dhrEp7l/Ex8VXs1HX/Fpd03Zj287DhTzzZSrhgZ78bXQvvN1danldLeetwzkb/bUNqvcKXwekbviR6MBiyE6CrZ9B0kfGBq+girDvZ/zbJhbcfWupUQhRX7Yd7h5+FHm3hZDujX7o9GMnufeb9fj7dWHWA1fj7eve6OewZ7nBpyAhwfjAUg7HdxlBn5Vk/LtnecWeCkIiL4R9eBwEdwUnuR0kREPYdrhbyaH8M4yftQlXZyfmTe5PSwn2hnFyhtCexhI70Vh3Jh8OpkB2shH2O/4Dmz8xtrn7Q5u+EBF/4ereS+afFaI+JNwvcuJ0CeNnbeTU2TI+f+gq2gZ5mV2SffIMgM7DjAWM5qPcdCPozy0//Q20xdge1LlSc068cbXvLN++QlyO/HRUUlRSxqTEJLJOnGHe5Hh6tPIzuyTHoRQEdzGWmPuMdWdPwaFfK8I+GdJXGu33AK5e0Lpv1eYcX5mEXIhzJNwrlJRZePjTzWzLzmfmuFj6dwwyuyTh7gMdBhoLGFf3+QeqXt2vnwGWUmN7QNsLQR8eB2HR4CJNasIxSbgDFovm6X9v5ac9x3njzl7c0DPM7JJEdZSCwHbGEj3aWFdaDEe2XQj7Axsh7Utjm7MbtOptNOOcu8L3D5dHMYVDcPhw11rzv9/t4D9bDvGn4d24Oy7C7JJEfbh6GDdeIyo9Dlt46MKN2uxkSJ4NG2YY23zCLgR9RDy0igE3ua8i7I/Dh/t7q/cy55dMplzbgUcGdzK7HNEY/FpD5K3GAlBeCkfTKgV+EuxaYmxTzhAWVbU5p0VHuboXNs+hw33hpgP8bcVubu/Thudv6oGSH2j75OwKrfsYS/wDxrrTOcajmFmbKjpaLYKkj41tni0qhX0/41FMD7m5LmyLw4b7iu1H+PPXqSR0a8kbo3vh5CTB7lC8g6HrjcYCFR2tdle9WfvbioqdFbTsbgyfcL6jVTfpaCWaNYcM9w0Zufz+s1/pHRHAe2P74uosP6QOz8kZQiONJfZ+Y92ZfDi0+UJzzs5vYfNcY5u7n9HRKjzuwg1b6WglmhGHC/fthwp44JNk2rXwYs7EOLzcHO5LIOrKMwA6DTUWqOhotbfq1f3Pb4EuN7a36HShKSciHkJ6SkcrYRqH+s47kFvE/bOT8PVwYe6UeAK83MwuSdgSpSC4s7HE3GusKzldtaPV3h9h20Jjm6uX0c5fpaOVPGYrmobDhPuxk8WMn72RcouFuQ9eTSt/GWdcNAI3b2h/rbGAcXVfkHUh7LM2wfr3LnS08o+o+mROq17S0UpYhUOEe2FxKRNnJ3H85FkWPDCAziE+Zpck7JVSRk/ZgLYQdaexrrQYjqRWas5Jhu1fGduc3SCs14Xx7sPjjF8A8uSWaCC7D/fi0nIenJvMnqMnmT0xjpiIALNLEo7G1cMI7oi4C+sKD8PBSh2tUhJh4/vGNp/QqmPet+5j/IUgRD3YdbiXWzRPLPyVDRl5vH1PDIO6tjS7JCEMfq3A7xbocYvxcXkpHN1+Iewv7mgV2rNqc05QJ7m6FzWy23DXWvPC4lRWbD/KS7dEMiqmjdklCXF5zq7QOsZYzne0yq0Y876io9W2zyF5lrHNM7Cajlb+5tUvmh27Dfe3ftjDZ5uy+N2Qzky6poPZ5QhRf95B0PUGYwGjo1XOnqpt97/9gDHloYKW3S6Mdx8eZ3zs5GzmZyBMZJfhPueXffzrx3TujY/gjzd0NbscIRqHkzOE9DCWvhOMdcUFcLBSR6tdS+HXT41tbr6VOlpVLN4ylLWjsLtw/8+Wg7zy7Q6G9wxj2m3RMl6MsG8e/tBpiLGA8ShmXkbVjlZr/1Gpo1XHqs05oVFGk5CwO3YV7mv2HOePn29lQMcW/POeGJxlvBjhaJQybrYGdYLe9xjrSorg8JYLg6RlrIZti4xtLp6XdrTya2Va+aLx2E24/3rgBI98mkLXUF8+nNAPD1dpaxQCMMarb3e1sUBFR6vsSk/mbIKNM2HdO8Z2v/Cqg6SF9TIe5xQ2xWrhrpQaDrwNOAMfa62nW+tc6cdOMTkxiZa+7nwyOR4/D/kzU4jLUgoCIowl6g5jXdnZqh2tspJg+9fGNidXoydt5bb7gLbyKGYzZ5VwV0o5AzOA64FsIEkp9Y3Wekdjnyuv2MKfZ23E2cmJeZP709JXunILUW8u7hVNM/2AR4x1J49UndFq81zjCh/AO+TSjlbu0vO7ObHWlXs8kK61zgBQSi0ERgGNGu6/HtnF/+1ZQomHE3fFRbA0O934VSJM5eLkQkh5iNlliIbyDYMeNxsLQHkZHNtR8dx9Rejv/s7YppyMjla5mbiVu0DObxDUWa7uTWStcG8DZFX6OBvoX3kHpdSDwIMAoaGhrF69ut4nWXQwmRL/HwD4Yu8VViqsYoTXCPxWy+xF9qkzBHaGwHtwKS3Er/A3/Ap341e4G33qGF7aAu/2o9TFh0K/bhT6daXQrxsnfbtQ5ipX9xc7derUFeVfbUy7oaq1/hD4EKBfv346ISGh3scYrAfz1fIYbrtxSCNXJ66URtN3Xl8srhau5D0Vtk19ncDJ3KNw659xzU4iKDuZoMyFGB2tMGawqjxIWsvuDt/RavXq1Vb5WbFWuB8EIip9HF6xrlEppQjydMHZwb85mhtPF09KLCVmlyFMUu7sDn3HGwtAcWHFjFYVbfd7lsGWcx2tfKrpaBVsXvF2xFrhngR0UUp1wAj1e4D7rHQu0cx4uXpxVp81uwzRXHj4QccEY4FKHa2SLzyd88vbYCkztgd2qNrRKixaOlpdAauEu9a6TCn1O2AFxqOQs7XW261xLtH8eLp4crZcwl1cRpWOVmOMdSVFcHjrhUHS9v0EqZ8b21w8oFVM1Wfv/VqbV7+NsFqbu9Z6KbDUWscXzZe3qzdbTm5h0MJBZpcimti2Y9uwaEvD3/vwUNDBxtV8eRlYjkD215BdMcmJcjKev3d2AaeKBdt8Mudqj6tJIKHRj2s3PVRF8/FI70f4d9K/ad1Grq4cTZZHFiVnS7ih/Q2Nf3CLBYpy4fQxOFWxlJwwtikn8Aoynr/3qVjcfRu/BivwzbNOnRLuotENbTsUpwwnEgYkmF2KaGIr/VaSn5/PCwNeaJoTnjxadUar9BQoLTK2ebe8qKNV32bZ0coaj0GChLsQwpb5hkL3kcYCRhPO8Z0Vg6Sd62hV0TqsnCAk8qIZrTqDk5N59VuRhLsQwn44uxhP14RFQ9wUY11RXsWY90nGDdu0ryBljrHNwx/a9Lvw7H2bWGOWKzsg4S6EsG9eLaDLdcYCRtt97m9VZ7T66Q3QFmN7cNdKzTnxxuQoNtiXRsJdCOFYnJyMKQhbdoM+44x1Z09WurpPhj3LYct8Y5ur96UdrXxamld/HUm4CyGEuy90HGwsYHS0OpFZdUarde9U6mjV/qIZraLBxc2s6qsl4S6EEBdTClp0MJZedxvrSs9UdLRKMm7YZq6F1C+Mbc7u0Dqm6tW9fxvz6kfCXQgh6sbVE9oOMJZzCg5Wbbvf9BGsf9fY5tu66vSFrWOMYzQRCXchhLhS/m2MpedtxsdlJXA0teq4OTu/MbY5VTzJU7k5J7CD1UqTcBdCiMbi4mY8TtkmFvo/ZKw7daxq2P86HzZ9aGzzCia81S0gww8IIYSN8QmB7jcZC4ClHI7tPB/2JWdbWOW0Eu5CCNGUnJwhLMpY+k3i2OrVRFrjNFY4phBCCJNJuAshhB2ScBdCCDsk4S6EEHZIwl0IIeyQhLsQQtghCXchhLBDEu5CCGGHlNba7BpQSh0H9l/hy4OBnEYsRzQOeV8cl7z39dOQr1c7rXW1g8s3i3BvCKVUsta6n9l1iKrkfXFc8t7Xj7W+XtIsI4QQdkjCXQgh7JA9hPuHZhcgqiXvi+OS975+rPL1svk2dyGEEJeyhyt3IYQQF5FwF0IIO2TT4a6UGq6U2q2USldKPWt2PcKglHJWSv2qlFpidi2i6SilnlBKpSmltiul/mB2Pc2RUmq2UuqYUiqt0rq/KaV2KaW2KaW+VkoFNMa5bDbclVLOwAxgBBAJ3KuUssaEJqL+ngB2ml2EaDpKqSjgASAe6A3crJTqbG5VzVIiMPyidT8AUVrrXsAe4LnGOJHNhjvGN1G61jpDa10CLARGmVyTw1NKhQMjgY/NrkU0qR7ARq11kda6DFgD3GFyTc2O1vonIO+idd9XfM0ANgDhjXEuWw73NkBWpY+zK9YJc/0T+BNgMbsQ0aTSgIFKqSCllBdwExBhck22aDKwrDEOZMvhLpoZpdTNwDGtdYrZtYimpbXeCbwOfA8sB7YA5aYWZWOUUs8DZcD8xjieLYf7QapeGYRXrBPmuQa4VSmVidFMNlQp9am5JYmmorWepbWO1VoPAk5gtB+LOlBKTQRuBsbqRup8ZMvhngR0UUp1UEq5AfcA35hck0PTWj+ntQ7XWrfHeD9+1FqPM7ks0USUUiEV/7bFaG9fYG5FtkEpNRyjKfNWrXVRYx3XpbEO1NS01mVKqd8BKwBnYLbWervJZQnhyL5USgUBpcBjWut8swtqbpRSnwEJQLBSKht4CePpGHfgB6UUwAat9cMNPpcMPyCEEPbHlptlhBBCXIaEuxBC2CEJdyGEsEMS7kIIYYck3IUQwg5JuAshhB2ScBcOSykVoJR69DLb2iulziilttRyjPlKqTyl1GjrVCnElZFwF44sAKg23Cvs1VrH1HQArfVYpGe0aIYk3IUjmw50UkptUUr9raYdlVLeSqnvlFJbKyakGNNENQpxRWx2+AEhGsGzGJMk1Hh1XmE4cEhrPRJAKeVv1cqEaCC5cheiblKB65VSryulBmqtC8wuSIiaSLgLUQda6z1AX4yQn6aUetHkkoSokTTLCEd2EvCty45KqdZAntb6U6VUPjDVqpUJ0UAS7sJhaa1zlVK/VMxEv0xr/XQNu0cDf1NKWTCGtH2kSYoU4gpJuAuHprW+r477rcCYO0AImyBt7kJUrxzwr0snJmAwUNwkVQlRRzJZhxBC2CG5chdCCDsk4S6EEHZIwl0IIeyQhLsQQtih/wci62b18JCu9QAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Naloga 2\n",
        "Ravninsko gibanje točke je definirano z $v_{x}(t)=50-16\\,t$ in $y(t)=100-4\\,t^{2}$, kjer je $v_{x}$ v [m/s], $t$ v [s] in $y$ v [m]. Znano je tudi, da je točka pri času $t=0$ s na položaju $x=0$.\n",
        " - Narišite pot, ki jo opravi točka.\n",
        " - Določite in narišite hitrost in pospešek, ko je dosežen položaj $y=0$."
      ],
      "metadata": {
        "id": "s-pGJqTtj4A2"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def položaj_x(t):\n",
        "  return -8*t**2 + 50*t\n",
        "\n",
        "def položaj_y(t):\n",
        "  return 100 - 4*t**2"
      ],
      "metadata": {
        "id": "yrTAXQj8iyKA"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "t_točke = np.array([0, 1, 2, 3, 4, 5])\n",
        "x_točke = položaj_x(t_točke)\n",
        "y_točke = položaj_y(t_točke)\n",
        "\n",
        "t = np.arange(0, 5, 0.001)\n",
        "x = položaj_x(t)\n",
        "y = položaj_y(t)"
      ],
      "metadata": {
        "id": "msZ5LEV7kYoc"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.plot(x, y)\n",
        "ax.scatter(x_točke, y_točke, marker = \"o\", c=\"C1\", zorder = 10)\n",
        "ax.set_aspect('equal')\n",
        "plt.grid()\n",
        "plt.xlabel(\"x [m]\")\n",
        "plt.ylabel(\"y [m]\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "1VNO3zV5kzBI",
        "outputId": "c70ea33c-35c0-473e-cacd-467c2d468d23"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'y [m]')"
            ]
          },
          "metadata": {},
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Naloga 3\n",
        "Pilot letala bi rad odvrgel paket na točko A. Izračunajte kot $\\theta$ med direktno linijo (letalo - točka A) pri času, ki bi moral pilot izpustiti paket."
      ],
      "metadata": {
        "id": "SkKM9rfAjbq0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "vx = 500/3.6\n",
        "g = 9.81;\n",
        "L=100\n",
        "\n",
        "t = np.arange(0, 5, 0.01)\n",
        "\n",
        "x = vx*t\n",
        "y = -g*t**2/2 + L"
      ],
      "metadata": {
        "id": "Zz7N5t8olHAP"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.plot(x, y)\n",
        "ax.set_aspect('equal')\n",
        "plt.grid()\n",
        "plt.xlabel(\"x [m]\")\n",
        "plt.ylabel(\"y [m]\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 139
        },
        "id": "MLBGxGchkou5",
        "outputId": "51d0dacb-1ad1-4085-cc79-e802cfefbbb7"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'y [m]')"
            ]
          },
          "metadata": {},
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "ikYzQSH6kyVo"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}