DTU-Noter/10060 - Physics/Kinematics 1D/Kinematics1D notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0cce236a",
   "metadata": {},
   "source": [
    "### Examples of solution of kinematics 1D problems"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem\n",
    "\n",
    "A stone is thrown up in the air with initial velocity $v_1$. The stone is thrown from the height $h$ over the ground.\n",
    "\n",
    ">a) How long time does it take for the stone to reach its highest point?\n",
    "\n",
    ">b) How long time does it take for the stone to reach the ground?\n",
    "\n",
    ">c) What is the velocity at time of impact with the ground?\n",
    "\n",
    "\n",
    "For each problem we set up one or more symbolic equations in a general form, then substitute specific information in to the equation(s), and then we solve the equation(s). We print out the general solution(s), then select the proper solution (if there are more solutions)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "447993b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a)\n",
      "Equation:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle v_{2} = a t + v_{1}$"
      ],
      "text/plain": [
       "Eq(v_2, a*t + v_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equation after substitution:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0 = - g t + v_{1}$"
      ],
      "text/plain": [
       "Eq(0, -g*t + v_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[v_1/g]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final solution:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{v_{1}}{g}$"
      ],
      "text/plain": [
       "v_1/g"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import symbols,Eq,solve,Rational\n",
    "print('a)')\n",
    "t,y1,y2,v1,v2,a,g,h = symbols('t,y_1,y_2,v_1,v_2,a,g,h')\n",
    "eq = Eq(v2,v1+a*t)\n",
    "print('Equation:')\n",
    "display(eq)\n",
    "print('Equation after substitution:')\n",
    "eq = eq.subs({a:-g,v2:0})\n",
    "display(eq)\n",
    "sol = solve(eq,t)\n",
    "print('Solution:')\n",
    "display(sol)\n",
    "print('Final solution:')\n",
    "display(sol[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b)\n",
      "Equation:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y_{2} = \\frac{a t^{2}}{2} + t v_{1} + y_{1}$"
      ],
      "text/plain": [
       "Eq(y_2, a*t**2/2 + t*v_1 + y_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equation after substitution:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0 = - \\frac{g t^{2}}{2} + h + t v_{1}$"
      ],
      "text/plain": [
       "Eq(0, -g*t**2/2 + h + t*v_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[(v_1 - sqrt(2*g*h + v_1**2))/g, (v_1 + sqrt(2*g*h + v_1**2))/g]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final solution:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{v_{1} + \\sqrt{2 g h + v_{1}^{2}}}{g}$"
      ],
      "text/plain": [
       "(v_1 + sqrt(2*g*h + v_1**2))/g"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import symbols,Eq,solve,Rational\n",
    "print('b)')\n",
    "t,y1,y2,v1,v2,a,g,h = symbols('t,y_1,y_2,v_1,v_2,a,g,h')\n",
    "eq = Eq(y2,y1+v1*t+Rational(1,2)*a*t**2)\n",
    "print('Equation:')\n",
    "display(eq)\n",
    "print('Equation after substitution:')\n",
    "eq = eq.subs({a:-g,y1:h,y2:0})\n",
    "display(eq)\n",
    "sol = solve(eq,t)\n",
    "print('Solution:')\n",
    "display(sol)\n",
    "print('Final solution:')\n",
    "display(sol[1])\n",
    "t_impact = sol[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c)\n",
      "Equations:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y_{2} = \\frac{a t^{2}}{2} + t v_{1} + y_{1}$"
      ],
      "text/plain": [
       "Eq(y_2, a*t**2/2 + t*v_1 + y_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle v_{2} = a t + v_{1}$"
      ],
      "text/plain": [
       "Eq(v_2, a*t + v_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equation after substitution:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0 = - \\frac{g t^{2}}{2} + h + t v_{1}$"
      ],
      "text/plain": [
       "Eq(0, -g*t**2/2 + h + t*v_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle v_{2} = - g t + v_{1}$"
      ],
      "text/plain": [
       "Eq(v_2, -g*t + v_1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[((v_1 - sqrt(2*g*h + v_1**2))/g, sqrt(2*g*h + v_1**2)),\n",
       " ((v_1 + sqrt(2*g*h + v_1**2))/g, -sqrt(2*g*h + v_1**2))]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final solution:\n",
      "Time to impact\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{v_{1} + \\sqrt{2 g h + v_{1}^{2}}}{g}$"
      ],
      "text/plain": [
       "(v_1 + sqrt(2*g*h + v_1**2))/g"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Velocity at impact\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\sqrt{2 g h + v_{1}^{2}}$"
      ],
      "text/plain": [
       "-sqrt(2*g*h + v_1**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import symbols,Eq,solve,Rational\n",
    "print('c)')\n",
    "t,y1,y2,v1,v2,a,g,h = symbols('t,y_1,y_2,v_1,v_2,a,g,h')\n",
    "eq1 = Eq(y2,y1+v1*t+Rational(1,2)*a*t**2)\n",
    "eq2 = Eq(v2,v1+a*t)\n",
    "print('Equations:')\n",
    "display(eq1)\n",
    "display(eq2)\n",
    "print('Equation after substitution:')\n",
    "eq1 = eq1.subs({a:-g,y1:h,y2:0})\n",
    "eq2 = eq2.subs({a:-g,y1:h,y2:0})\n",
    "display(eq1)\n",
    "display(eq2)\n",
    "sol = solve([eq1,eq2],[t,v2])\n",
    "print('Solution:')\n",
    "display(sol)\n",
    "print('Final solution:')\n",
    "print('Time to impact')\n",
    "display(sol[1][0])\n",
    "print('Velocity at impact')\n",
    "display(sol[1][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem\n",
    "\n",
    "A cyclist travels with the velocity as shown in the figure below.\n",
    "\n",
    ">a) How far does the cyclist travel in the time interval?\n",
    "\n",
    ">b) How far does the cyclist travel in the time interval from 13 s to 52 s?\n",
    "\n",
    ">c) What is the average velocity of the cyclist in the time interval from 0 s to 25 s?\n",
    "\n",
    "Note the way in which the velocity is calculated. Since it is a piecewise defined function we use *if*s in the definition of *f(t)*. \n",
    "We then use list comprehension to compute the velocity for each time in the time vector *t*.\n",
    "List comprehension uses *[v(T) for T in t if True]*, it goes through all values in *t* and if *True* (always, true) it adds *v(T)* to the list.\n",
    "The function *f(t)* cannot be called with a vector argument (try it).\n",
    "\n",
    "The problem can be solved by computing the area under the curve, we do it numerically, but you can also do it manually.\n",
    "Here we employ the method *quad* from *scipy.integrate*. This method return the value of the integral and the estimated uncertainty.\n",
    "In our case we have a function that can be evaluated at all points. If we only had data (x,y) to integrate over the method *trapezoid* can be used, we show how to use it in a)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "t = np.linspace(0,60,1000)\n",
    "def f(t):\n",
    "    if t < 20:\n",
    "        return 0.5 * t\n",
    "    elif t < 50:\n",
    "        return 10.0\n",
    "    else:\n",
    "        return 10.0 - 1.0 * (t-50.0)\n",
    "v = [f(T) for T in t if True]\n",
    "plt.figure()\n",
    "plt.plot(t,v,'b-')\n",
    "plt.xlabel('Time $t$ (s)')\n",
    "plt.ylabel('Velocity $v$ (m/s)')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a) - uses integration with function\n",
      "450.0\n",
      "4.996003610813204e-13\n",
      "   - uses integration with data\n",
      "449.99954909864823\n"
     ]
    }
   ],
   "source": [
    "from scipy.integrate import quad,trapezoid\n",
    "print('a) - uses integration with function')\n",
    "distance,uncertainty = quad(f,0.0,60.0)\n",
    "print(distance)\n",
    "print(uncertainty)\n",
    "print('   - uses integration with data')\n",
    "distance = trapezoid(v,t)\n",
    "print(distance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "t = np.linspace(0,60,1000)\n",
    "def f(t):\n",
    "    if t < 20:\n",
    "        return 0.5 * t\n",
    "    elif t < 50:\n",
    "        return 10.0\n",
    "    else:\n",
    "        return 10.0 - 1.0 * (t-50.0)\n",
    "v = np.array([f(T) for T in t if True])\n",
    "x = np.array([T for T in t if T>=13 and T<=52]) # select the times in the interval [13,52]\n",
    "y = np.array([f(T) for T in t if T>=13 and T<=52]) # select the function values for the times in the interval [13,52]\n",
    "plt.figure()\n",
    "plt.plot(t,v,'b-')\n",
    "plt.fill_between(x,0,y,alpha=0.3)\n",
    "plt.xlabel('Time $t$ (s)')\n",
    "plt.ylabel('Velocity $v$ (m/s)')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b)\n",
      "375.74999999039994\n",
      "1.4357277387263215e-06\n"
     ]
    }
   ],
   "source": [
    "print('b)')\n",
    "distance,uncertainty = quad(f,13.0,52.0)\n",
    "print(distance)\n",
    "print(uncertainty)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c)\n",
      "5.999999999999999\n"
     ]
    }
   ],
   "source": [
    "print('c)')\n",
    "distance,uncertainty = quad(f,0.0,25.0)\n",
    "print(distance/25.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6342f72e",
   "metadata": {},
   "source": [
    "#### Problem\n",
    "\n",
    "A train travls with the speed $20$ m/s and is at time $t=0$ at $x=0$ m. \n",
    "Another train is at time $t=0$ at $x=100$ m. \n",
    "The secon train travels with velocity $-20$ m/s. \n",
    "The two train are on course for a collision, and the train driver of the second train\n",
    "start breaking with an acceleration of $0.5 \\text{m/s}^2$.\n",
    "\n",
    ">a) Determine the time at which the trains collide (if they do)? Comment on the solution(s).\n",
    "\n",
    ">b) Graph the positions of the trains as a function of time for $t\\in[0 s,200 s]$?\n",
    "\n",
    ">c) What happens if the acceleration is $2.5 \\text{m/s}^2$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2eca09f1",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a)\n",
      "Equation:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle t v_{1} + x_{10} = \\frac{a_{2} t^{2}}{2} + t v_{2} + x_{20}$"
      ],
      "text/plain": [
       "Eq(t*v1 + x10, a2*t**2/2 + t*v2 + x20)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equation after substitution:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 20 t = 0.25 t^{2} - 20 t + 400$"
      ],
      "text/plain": [
       "Eq(20*t, 0.25*t**2 - 20*t + 400)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[10.7179676972449, 149.282032302755]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final solution:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 10.7179676972449$"
      ],
      "text/plain": [
       "10.7179676972449"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The first solution is an impact, the second solution is like the second train passed through the second train and impacted a second time.\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols,Eq,solve,Rational\n",
    "print('a)')\n",
    "x10,v1,x20,v2,a2,t = symbols('x10,v1,x20,v2,a2,t')\n",
    "x1 = x10 + v1 * t\n",
    "x2 = x20 + v2 * t + Rational(1,2) * a2 * t**2\n",
    "eq = Eq(x1,x2)\n",
    "print('Equation:')\n",
    "display(eq)\n",
    "eq = eq.subs({x10:0,x20:400,v1:20,v2:-20,a2:0.5})\n",
    "print('Equation after substitution:')\n",
    "display(eq)\n",
    "print('Solution:')\n",
    "sol = solve(eq,t)\n",
    "display(sol)\n",
    "print('Final solution:')\n",
    "display(sol[0])\n",
    "print('The first solution is an impact, the second solution is like the second train passed through the second train and impacted a second time.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e0b44c34",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('b)')\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure()\n",
    "t = np.linspace(0,20,1000)\n",
    "x1 = 20*t\n",
    "x2 = 400 -20*t+0.5*0.5*t**2\n",
    "plt.plot(t,x1,'b-',label='$x_1$')\n",
    "plt.plot(t,x2,'g-',label='$x_2$')\n",
    "plt.xlabel('Time $t$ (s)')\n",
    "plt.ylabel('Positions $x$(m)')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "t = np.linspace(0,200,1000)\n",
    "x1 = 20*t\n",
    "x2 = 400 -20*t+0.5*0.5*t**2\n",
    "x1 = 20*t\n",
    "x2 = 400 -20*t+0.5*0.5*t**2\n",
    "plt.plot(t,x1,'b-',label='$x_1$')\n",
    "plt.plot(t,x2,'g-',label='$x_2$')\n",
    "plt.xlabel('Time $t$ (s)')\n",
    "plt.ylabel('Positions $x$ (m)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "59c9b6a1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c)\n",
      "Equation:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle t v_{1} + x_{10} = \\frac{a_{2} t^{2}}{2} + t v_{2} + x_{20}$"
      ],
      "text/plain": [
       "Eq(t*v1 + x10, a2*t**2/2 + t*v2 + x20)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equation after substitution:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 20 t = 1.25 t^{2} - 20 t + 400$"
      ],
      "text/plain": [
       "Eq(20*t, 1.25*t**2 - 20*t + 400)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[16.0 - 8.0*I, 16.0 + 8.0*I]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are no real solutions, hence no impact.\n"
     ]
    }
   ],
   "source": [
    "print('c)')\n",
    "from sympy import symbols,Eq,solve,Rational\n",
    "x10,v1,x20,v2,a2,t = symbols('x10,v1,x20,v2,a2,t')\n",
    "x1 = x10 + v1 * t\n",
    "x2 = x20 + v2 * t + Rational(1,2) * a2 * t**2\n",
    "eq = Eq(x1,x2)\n",
    "print('Equation:')\n",
    "display(eq)\n",
    "eq = eq.subs({x10:0,x20:400,v1:20,v2:-20,a2:2.5})\n",
    "print('Equation after substitution:')\n",
    "display(eq)\n",
    "sol = solve(eq,t)\n",
    "print('Solution:')\n",
    "display(sol)\n",
    "print('There are no real solutions, hence no impact.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "81c65613",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure()\n",
    "t = np.linspace(0,20,1000)\n",
    "x1 = 20*t\n",
    "x2 = 400 -20*t+0.5*2.5*t**2\n",
    "plt.plot(t,x1,'b-',label='$x_1$')\n",
    "plt.plot(t,x2,'g-',label='$x_2$')\n",
    "plt.xlabel('$t$ (s)')\n",
    "plt.ylabel('Position (m)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}