{"id":2322,"date":"2026-10-01T05:02:25","date_gmt":"2026-09-30T22:02:25","guid":{"rendered":"https:\/\/people.usd.ac.id\/~ydkristanto\/?page_id=2322"},"modified":"2026-10-05T19:12:16","modified_gmt":"2026-10-05T12:12:16","slug":"exploring-motion-on-an-inclined-plane","status":"publish","type":"page","link":"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-motion-on-an-inclined-plane\/","title":{"rendered":"Exploring Motion on an Inclined Plane"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-right\">\n<div class=\"wp-block-button is-style-outline\"><a class=\"wp-block-button__link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/media-pengajaran\/eksplorasi-gerak-pada-bidang-miring\/\">ID<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"has-drop-cap\">What affects the motion of an object on an inclined plane? What happens when you change its initial velocity, friction, or the angle of inclination? Explore the simulation to investigate how different conditions affect the object&#8217;s motion as represented by the graph of its displacement over time.<\/p>\n\n\n\n<div class=\"wp-block-group alignfull has-gray-background-color has-background\"><div class=\"wp-block-group__inner-container\">\n<h3 class=\"has-text-align-center\">Seeing the Motion Through Graph<\/h3>\n\n\n\n<p>Adjust the parameters, play the animation, and see how the object&#8217;s motion is represented in its displacement-time graph.<\/p>\n\n\n\n<div class=\"wp-block-columns alignwide\">\n<div class=\"wp-block-column\">\n<figure>\n<div id=\"calculator1\" class=\"aligncenter size-full\" style=\"width: 440px; height: 440px;\"><\/div>\n<figcaption>Visualization 1: Object motion on an inclined plane<\/figcaption>\n<\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<figure>\n<div id=\"calculator2\" class=\"aligncenter size-full\" style=\"width: 440px; height: 440px;\"><\/div>\n<figcaption>Visualization 2: The graph of displacement over time<\/figcaption>\n<\/figure>\n\n\n<script>\n  var calculator1 = Desmos.GraphingCalculator(document.getElementById('calculator1'), {\n    expressions: false,\n    settingsMenu: false,\n    trace: false\n  });\n  var calculator2 = Desmos.GraphingCalculator(document.getElementById('calculator2'), {\n    expressions: false,\n    settingsMenu: false\n  });\n\n  var state1 = {\n    \"version\": 11,\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -10,\n            \"ymin\": -8.73513881416078,\n            \"xmax\": 10,\n            \"ymax\": 12.735138814160777\n        },\n        \"showGrid\": false,\n        \"showXAxis\": false,\n        \"showYAxis\": false,\n        \"userLockedViewport\": true,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-10\",\n            \"xmax\": \"10\",\n            \"ymin\": \"-8.73513881416078\",\n            \"ymax\": \"12.735138814160777\"\n        }\n    },\n    \"expressions\": {\n        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\"id\": \"73\",\n                \"folderId\": \"28\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"s\\\\left(x\\\\right)=\\\\left\\\\{0\\\\le I\\\\le1:s_{A}\\\\left(x\\\\right),1<I\\\\le3:s_{B}\\\\left(x\\\\right),I=4:s_{C1}\\\\left(x\\\\right),I=5:s_{C2}\\\\left(x\\\\right)\\\\right\\\\}\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"61\",\n                \"folderId\": \"28\",\n                \"text\": \"# Case A \u2014 initially at rest\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"62\",\n                \"folderId\": \"28\",\n                \"color\": \"#c74440\",\n                \"latex\": \"s_{A}\\\\left(x\\\\right)=\\\\left\\\\{\\\\tan\\\\left(\\\\theta_{r}\\\\right)\\\\le 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\"color\": \"#388c46\",\n                \"latex\": \"c_{planeFill}=\\\\operatorname{rgb}\\\\left(203,213,225\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"83\",\n                \"folderId\": \"80\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"c_{planeStroke}=\\\\operatorname{rgb}\\\\left(71,85,105\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"84\",\n                \"folderId\": \"80\",\n                \"color\": \"#000000\",\n                \"latex\": \"c_{objectFill}=\\\\operatorname{rgb}\\\\left(59,130,246\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"85\",\n                \"folderId\": \"80\",\n                \"color\": \"#c74440\",\n                \"latex\": \"c_{objectStroke}=\\\\operatorname{rgb}\\\\left(29,78,216\\\\right)\"\n            },\n      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       \"color\": \"#2d70b3\",\n                \"latex\": \"c_{white}=\\\\operatorname{rgb}\\\\left(255,255,255\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"183\",\n                \"folderId\": \"80\",\n                \"color\": \"#c74440\",\n                \"latex\": \"c_{pink}=\\\\operatorname{rgb}\\\\left(214,90,111\\\\right)\"\n            }\n        ],\n        \"ticker\": {\n            \"handlerLatex\": \"\\\\left\\\\{P_{lay}=1:p_{lay}\\\\left(\\\\operatorname{dt}\\\\right),p_{lay}\\\\left(0\\\\right)\\\\right\\\\}\",\n            \"playing\": true,\n            \"open\": true\n        }\n    },\n    \"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true,\n    \"backmigrated\": 14\n};\n  var state2 = {\n    \"version\": 11,\n    \"randomSeed\": \"864e29efbc0f571619e4df2902f921c9\",\n    \"graph\": {\n        \"viewport\": {\n            \"xmin\": -1,\n            \"ymin\": -10,\n            \"xmax\": 5,\n            \"ymax\": 20\n        },\n        \"xAxisArrowMode\": \"POSITIVE\",\n        \"yAxisArrowMode\": \"POSITIVE\",\n        \"xAxisLabel\": \"Time (s)\",\n        \"yAxisLabel\": \"Displacement (m)\",\n        \"userLockedViewport\": true,\n        \"squareAxes\": false,\n        \"__v12ViewportLatexStash\": {\n            \"xmin\": \"-1\",\n            \"xmax\": \"5\",\n            \"ymin\": \"-10\",\n            \"ymax\": \"20\"\n        }\n    },\n    \"expressions\": {\n        \"list\": [\n            {\n                \"type\": \"folder\",\n                \"id\": \"2\",\n                \"title\": \"Given\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"1\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"t_{s}=3.9\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"min\": \"0\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"3\",\n                \"folderId\": \"2\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"v_{0}=-10\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"4\",\n                \"folderId\": \"2\",\n                \"color\": \"#388c46\",\n                \"latex\": \"g=9.81\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"5\",\n                \"folderId\": \"2\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"m=1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"6\",\n                \"folderId\": \"2\",\n                \"color\": \"#000000\",\n                \"latex\": \"m_{us}=0.4\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"7\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"m_{uk}=0.2\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"43\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"s_{r}=0.63\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"\\\\frac{\\\\pi}{2}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"119\",\n                \"folderId\": \"2\",\n                \"color\": \"#c74440\",\n                \"latex\": \"m_{state}=1\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"1\",\n                    \"max\": \"5\",\n                    \"step\": \"0\"\n                }\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"45\",\n                \"folderId\": \"2\",\n                \"text\": \"Conversion:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"8\",\n                \"folderId\": \"2\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"\\\\theta_{r}=s_{r}\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"\\\\frac{\\\\pi}{2}\"\n                }\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"10\",\n                \"title\": \"Model\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"19\",\n                \"folderId\": \"10\",\n                \"text\": \"Conditions:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"20\",\n                \"folderId\": \"10\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"I_{1}=\\\\left\\\\{v_{0}=0:0,v_{0}>0:2,4\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"21\",\n                \"folderId\": \"10\",\n                \"color\": \"#388c46\",\n                \"latex\": \"I_{2}=\\\\left\\\\{\\\\tan\\\\left(\\\\theta_{r}\\\\right)\\\\le m_{us}:0,1\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"22\",\n                \"folderId\": \"10\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"I=I_{1}+I_{2}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"24\",\n                \"folderId\": \"10\",\n                \"text\": \"Displacement over time:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"25\",\n                \"folderId\": \"10\",\n                \"color\": \"#c74440\",\n                \"latex\": \"s\\\\left(x\\\\right)=\\\\left\\\\{0\\\\le I\\\\le1:s_{A}\\\\left(x\\\\right),1<I\\\\le3:s_{B}\\\\left(x\\\\right),I=4:s_{C1}\\\\left(x\\\\right),I=5:s_{C2}\\\\left(x\\\\right)\\\\right\\\\}\",\n                \"hidden\": true,\n                \"colorLatex\": \"c_{blue}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"28\",\n                \"folderId\": \"10\",\n                \"text\": \"# Case A \u2014 initially at rest\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"29\",\n                \"folderId\": \"10\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"s_{A}\\\\left(x\\\\right)=\\\\left\\\\{\\\\tan\\\\left(\\\\theta_{r}\\\\right)\\\\le m_{us}:0,\\\\frac{1}{2}g\\\\left(\\\\sin\\\\left(\\\\theta_{r}\\\\right)-m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)\\\\right)x^{2}\\\\right\\\\}\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"31\",\n                \"folderId\": \"10\",\n                \"text\": \"# Case B \u2014 initially moving downhill\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"32\",\n                \"folderId\": \"10\",\n                \"color\": \"#c74440\",\n                \"latex\": \"s_{B}\\\\left(x\\\\right)=\\\\left\\\\{\\\\tan\\\\theta_{r}\\\\ge m_{uk}:v_{0}x+\\\\frac{1}{2}g\\\\left(\\\\sin\\\\left(\\\\theta_{r}\\\\right)-m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)\\\\right)x^{2},\\\\left\\\\{0\\\\le x\\\\le t_{Bstop}:v_{0}x+\\\\frac{1}{2}g\\\\left(\\\\sin\\\\left(\\\\theta_{r}\\\\right)-m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)\\\\right)x^{2},s_{Bstop}\\\\right\\\\}\\\\right\\\\}\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"130\",\n                \"folderId\": \"10\",\n                \"color\": \"#c74440\",\n                \"latex\": \"t_{Bstop}=\\\\frac{v_{0}}{g\\\\left(m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)-\\\\sin\\\\left(\\\\theta_{r}\\\\right)\\\\right)}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"131\",\n                \"folderId\": \"10\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"s_{Bstop}=v_{0}t_{Bstop}+\\\\frac{1}{2}g\\\\left(\\\\sin\\\\left(\\\\theta_{r}\\\\right)-m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)\\\\right)\\\\left(t_{Bstop}\\\\right)^{2}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"34\",\n                \"folderId\": \"10\",\n                \"text\": \"# Case C \u2014 initially moving uphill\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"35\",\n                \"folderId\": \"10\",\n                \"color\": \"#388c46\",\n                \"latex\": \"t_{stop}=\\\\frac{-v_{0}}{g\\\\left(\\\\sin\\\\left(\\\\theta_{r}\\\\right)+m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)\\\\right)}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"36\",\n                \"folderId\": \"10\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"s_{stop}=v_{0}t_{stop}+\\\\frac{1}{2}g\\\\left(\\\\sin\\\\left(\\\\theta_{r}\\\\right)+m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)\\\\right)t_{stop}^{2}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"37\",\n                \"folderId\": \"10\",\n                \"color\": \"#000000\",\n                \"latex\": \"s_{C1}\\\\left(x\\\\right)=\\\\left\\\\{0\\\\le x\\\\le t_{stop}:v_{0}x+\\\\frac{1}{2}g\\\\left(\\\\sin\\\\left(\\\\theta_{r}\\\\right)+m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)\\\\right)x^{2},x>t_{stop}:s_{stop}\\\\right\\\\}\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"38\",\n                \"folderId\": \"10\",\n                \"color\": \"#c74440\",\n                \"latex\": \"s_{C2}\\\\left(x\\\\right)=\\\\left\\\\{0\\\\le x\\\\le t_{stop}:v_{0}x+\\\\frac{1}{2}g\\\\left(\\\\sin\\\\left(\\\\theta_{r}\\\\right)+m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)\\\\right)x^{2},x>t_{stop}:s_{stop}+\\\\frac{1}{2}g\\\\left(\\\\sin\\\\left(\\\\theta_{r}\\\\right)-m_{uk}\\\\cos\\\\left(\\\\theta_{r}\\\\right)\\\\right)\\\\left(x-t_{stop}\\\\right)^{2}\\\\right\\\\}\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"40\",\n                \"title\": \"Graphs\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"41\",\n                \"folderId\": \"40\",\n                \"color\": \"#388c46\",\n                \"latex\": \"f\\\\left(x\\\\right)=s\\\\left(x\\\\right)\\\\left\\\\{0\\\\le x\\\\le t_{s}\\\\right\\\\}\",\n                \"hidden\": true,\n                \"colorLatex\": \"c_{blue}\",\n                \"lineWidth\": \"3\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"123\",\n                \"folderId\": \"40\",\n                \"text\": \"Cues:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"124\",\n                \"folderId\": \"40\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=0\\\\left\\\\{0\\\\le x\\\\le t_{s}\\\\right\\\\}\",\n                \"lineOpacity\": \".4\",\n                \"lineWidth\": \"5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"125\",\n                \"folderId\": \"40\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"x=0\\\\left\\\\{0\\\\le y\\\\le f\\\\left(t_{s}\\\\right)\\\\right\\\\}\\\\left\\\\{0\\\\le f\\\\left(t_{s}\\\\right)\\\\right\\\\}\",\n                \"colorLatex\": \"c_{blue}\",\n                \"lineOpacity\": \".4\",\n                \"lineWidth\": \"5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"126\",\n                \"folderId\": \"40\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"x=0\\\\left\\\\{f\\\\left(t_{s}\\\\right)\\\\le y\\\\le0\\\\right\\\\}\\\\left\\\\{0\\\\ge f\\\\left(t_{s}\\\\right)\\\\right\\\\}\",\n                \"colorLatex\": \"c_{blue}\",\n                \"lineOpacity\": \".4\",\n                \"lineWidth\": \"5\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"127\",\n                \"folderId\": \"40\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=t_{s}\\\\left\\\\{0\\\\le y\\\\le f\\\\left(t_{s}\\\\right)\\\\right\\\\}\\\\left\\\\{0\\\\le f\\\\left(t_{s}\\\\right)\\\\right\\\\}\",\n                \"lineStyle\": \"DASHED\",\n                \"lineOpacity\": \".6\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"128\",\n                \"folderId\": \"40\",\n                \"color\": \"#000000\",\n                \"latex\": \"x=t_{s}\\\\left\\\\{f\\\\left(t_{s}\\\\right)\\\\le y\\\\le0\\\\right\\\\}\\\\left\\\\{0\\\\ge f\\\\left(t_{s}\\\\right)\\\\right\\\\}\",\n                \"lineStyle\": \"DASHED\",\n                \"lineOpacity\": \".6\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"129\",\n                \"folderId\": \"40\",\n                \"color\": \"#000000\",\n                \"latex\": \"y=f\\\\left(t_{s}\\\\right)\\\\left\\\\{0\\\\le x\\\\le t_{s}\\\\right\\\\}\",\n                \"lineStyle\": \"DASHED\",\n                \"lineOpacity\": \".6\",\n                \"lineWidth\": \"1\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"121\",\n                \"folderId\": \"40\",\n                \"text\": \"The graph:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"42\",\n                \"folderId\": \"40\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"C=\\\\left(t_{s},f\\\\left(t_{s}\\\\right)\\\\right)\",\n                \"dragMode\": \"NONE\",\n                \"pointOutline\": true,\n                \"colorLatex\": \"c_{blue}\",\n                \"pointSize\": \"10\",\n                \"movablePointSize\": \"10\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"112\",\n                \"folderId\": \"40\",\n                \"color\": \"#c74440\",\n                \"latex\": \"r_{eset}=C_{list}\\\\to\\\\left[\\\\left(0,0\\\\right)\\\\right]\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"113\",\n                \"folderId\": \"40\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"C_{list}=\\\\left[\\\\left(0,0\\\\right)\\\\right]\",\n                \"hidden\": true\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"114\",\n                \"folderId\": \"40\",\n                \"color\": \"#388c46\",\n                \"latex\": \"i_{nList}\\\\left(L_{ist},P\\\\right)=\\\\left\\\\{\\\\operatorname{total}\\\\left(\\\\sum_{n=\\\\left[1...\\\\operatorname{length}\\\\left(L_{ist}\\\\right)\\\\right]}^{\\\\left[1...\\\\operatorname{length}\\\\left(L_{ist}\\\\right)\\\\right]}\\\\left\\\\{P.x=L_{ist}\\\\left[n\\\\right].x:\\\\left\\\\{P.y=L_{ist}\\\\left[n\\\\right].y:1,0\\\\right\\\\},0\\\\right\\\\}\\\\right)\\\\ge1:1,0\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"115\",\n                \"folderId\": \"40\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"a_{dd}=\\\\left\\\\{i_{nList}\\\\left(C_{list},C\\\\right)=0:C_{list}\\\\to\\\\operatorname{join}\\\\left(C_{list},C\\\\right)\\\\right\\\\}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"116\",\n                \"folderId\": \"40\",\n                \"color\": \"#000000\",\n                \"latex\": \"C_{show}=C_{list}\\\\left[2...\\\\operatorname{length}\\\\left(C_{list}\\\\right)\\\\right]\\\\left\\\\{\\\\operatorname{length}\\\\left(C_{list}\\\\right)>1\\\\right\\\\}\",\n                \"colorLatex\": \"c_{blue}\",\n                \"pointOpacity\": \".8\"\n            },\n            {\n                \"type\": \"folder\",\n                \"id\": \"47\",\n                \"title\": \"Buttons\",\n                \"collapsed\": true\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"58\",\n                \"folderId\": \"47\",\n                \"text\": \"Scaling:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"82\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(x_{R}-0.5,0\\\\right)\",\n                \"pointSize\": \"6\",\n                \"movablePointSize\": \"6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"83\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(0,y_{T}-2\\\\right)\",\n                \"pointSize\": \"6\",\n                \"movablePointSize\": \"6\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"54\",\n                \"folderId\": \"47\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"p=\\\\frac{1}{5}\\\\left(x_{R}-x_{L}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"55\",\n                \"folderId\": \"47\",\n                \"color\": \"#388c46\",\n                \"latex\": \"l=\\\\frac{1}{15}\\\\left(y_{T}-y_{B}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"56\",\n                \"folderId\": \"47\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"d_{x}=\\\\frac{1}{60}\\\\left(x_{R}-x_{L}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"64\",\n                \"folderId\": \"47\",\n                \"color\": \"#c74440\",\n                \"latex\": \"d_{y}=\\\\frac{1}{50}\\\\left(y_{T}-y_{B}\\\\right)\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"59\",\n                \"folderId\": \"47\",\n                \"color\": \"#c74440\",\n                \"latex\": \"x_{R}=5\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"1\",\n                    \"max\": \"60\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"60\",\n                \"folderId\": \"47\",\n                \"color\": \"#2d70b3\",\n                \"latex\": \"x_{L}=-\\\\frac{1}{5}x_{R}\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"61\",\n                \"folderId\": \"47\",\n                \"color\": \"#388c46\",\n                \"latex\": \"y_{T}=20\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"5\",\n                    \"max\": \"100\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"62\",\n                \"folderId\": \"47\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"y_{B}=-\\\\frac{1}{2}y_{T}\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"53\",\n                \"folderId\": \"47\",\n                \"text\": \"Record\/stop:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"117\",\n                \"folderId\": \"47\",\n                \"color\": \"#c74440\",\n                \"latex\": \"r_{ecord}=0\",\n                \"slider\": {\n                    \"hardMin\": true,\n                    \"hardMax\": true,\n                    \"min\": \"0\",\n                    \"max\": \"1\",\n                    \"step\": \"1\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"63\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"C_{1}=\\\\left(x_{R}-d_{x},y_{T}-d_{y}\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"65\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"C_{2}=\\\\left(x_{R}-d_{x}-p,y_{T}-d_{y}\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"66\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"C_{3}=\\\\left(x_{R}-d_{x}-p,y_{T}-d_{y}-l\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"67\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"C_{4}=\\\\left(x_{R}-d_{x},y_{T}-d_{y}-l\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"68\",\n                \"folderId\": \"47\",\n                \"color\": \"#c74440\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(C_{1},C_{2},C_{3},C_{4}\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"c_{white}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"71\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(C_{1},C_{2},C_{3},C_{4}\\\\right)\",\n                \"fillOpacity\": \"0\",\n                \"lineWidth\": \"1.5\",\n                \"clickableInfo\": {\n                    \"enabled\": true,\n                    \"latex\": \"r_{ecord}\\\\to1-r_{ecord}\"\n                }\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"80\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{C_{1}.x+C_{2}.x}{2},\\\\frac{C_{1}.y+C_{4}.y}{2}\\\\left\\\\{r_{ecord}=0\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Record\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"118\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\left(\\\\frac{C_{1}.x+C_{2}.x}{2},\\\\frac{C_{1}.y+C_{4}.y}{2}\\\\left\\\\{r_{ecord}=1\\\\right\\\\}\\\\right)\",\n                \"showLabel\": true,\n                \"label\": \"Stop rec.\",\n                \"hidden\": true,\n                \"labelSize\": \".8\",\n                \"pointOpacity\": \".9\"\n            },\n            {\n                \"type\": \"text\",\n                \"id\": \"73\",\n                \"folderId\": \"47\",\n                \"text\": \"Clear:\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"74\",\n                \"folderId\": \"47\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"K_{1}=\\\\left(x_{R}-2d_{x}-p,y_{T}-d_{y}\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"75\",\n                \"folderId\": \"47\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"K_{2}=\\\\left(x_{R}-2d_{x}-2p,y_{T}-d_{y}\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"76\",\n                \"folderId\": \"47\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"K_{3}=\\\\left(x_{R}-2d_{x}-2p,y_{T}-d_{y}-l\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"77\",\n                \"folderId\": \"47\",\n                \"color\": \"#6042a6\",\n                \"latex\": \"K_{4}=\\\\left(x_{R}-2d_{x}-p,y_{T}-d_{y}-l\\\\right)\",\n                \"hidden\": true,\n                \"dragMode\": \"NONE\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": \"78\",\n                \"folderId\": \"47\",\n                \"color\": \"#000000\",\n                \"latex\": \"\\\\operatorname{polygon}\\\\left(K_{1},K_{2},K_{3},K_{4}\\\\right)\",\n                \"lines\": false,\n                \"colorLatex\": \"c_{white}\",\n                \"fillOpacity\": \"1\"\n            },\n            {\n                \"type\": \"expression\",\n                \"id\": 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\"includeFunctionParametersInRandomSeed\": true,\n    \"doNotMigrateMovablePointStyle\": true,\n    \"backmigrated\": 14\n};\n\n  calculator1.setState(state1);\n  calculator2.setState(state2);\n  \n  \/\/ Source\n  var tsVar = calculator1.HelperExpression({ latex: 't_{s}' });\n  var v0Par = calculator1.HelperExpression({ latex: 'v_{0}' });\n  var gPar = calculator1.HelperExpression({ latex: 'g' });\n  var mPar = calculator1.HelperExpression({ latex: 'm' });\n  var musPar = calculator1.HelperExpression({ latex: 'm_{us}' });\n  var mukPar = calculator1.HelperExpression({ latex: 'm_{uk}' });\n  var srPar = calculator1.HelperExpression({ latex: 's_{r}' });\n  var xR = calculator2.HelperExpression({ latex: 'x_{R}' });\n  var xL = calculator2.HelperExpression({ latex: 'x_{L}' });\n  var yT = calculator2.HelperExpression({ latex: 'y_{T}' });\n  var yB = calculator2.HelperExpression({ latex: 'y_{B}' });\n  \n  \/\/ Sink\n  tsVar.observe('numericValue', function() {\n    var value = tsVar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '1', latex: `t_{s}=${value}` });\n    }\n  });\n  v0Par.observe('numericValue', function() {\n    var value = v0Par.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '3', latex: `v_{0}=${value}` });\n    }\n  });\n  gPar.observe('numericValue', function() {\n    var value = gPar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '4', latex: `g=${value}` });\n    }\n  });\n  mPar.observe('numericValue', function() {\n    var value = mPar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '5', latex: `m=${value}` });\n    }\n  });\n  musPar.observe('numericValue', function() {\n    var value = musPar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '6', latex: `m_{us}=${value}` });\n    }\n  });\n  mukPar.observe('numericValue', function() {\n    var value = mukPar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '7', latex: `m_{uk}=${value}` });\n    }\n  });\n  srPar.observe('numericValue', function() {\n    var value = srPar.numericValue;\n    if (!isNaN(value)) {\n      calculator2.setExpression({ id: '43', latex: `s_{r}=${value}` });\n    }\n  });\n  \n  \/\/ Update graph bounds\nfunction updateBounds() {\n  var leftB = xL.numericValue;\n  var rightB = xR.numericValue;\n  var topB = yT.numericValue;\n  var bottomB = yB.numericValue;\n\n  if (!isNaN(leftB)) {\n    if (!isNaN(rightB)) {\n      calculator2.setMathBounds({\n        left: leftB,\n        right: rightB,\n        bottom: bottomB,\n        top: topB\n      });\n    }\n  }\n}\n\nxL.observe('numericValue', updateBounds);\nxR.observe('numericValue', updateBounds);\nyT.observe('numericValue', updateBounds);\nyB.observe('numericValue', updateBounds);\n  \n<\/script>\n<\/div>\n<\/div>\n\n\n\n<p>In <a href=\"#calculator2\">Visualization 2<\/a>, press &#8220;Record&#8221; to begin tracing the point as the object moves. Press &#8220;Stop rec.&#8221; to stop recording the trace while keeping the recorded points visible. Use &#8220;Clear&#8221; to remove the recorded trace.<\/p>\n<\/div><\/div>\n\n\n\n<h3>Ready for More?<\/h3>\n\n\n\n<p>Someone adjusts the parameters of the simulation and, when the animation is played, obtains a graph like the one shown in <a href=\"#figure1\">Figure 1<\/a>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\" id=\"figure1\"><img loading=\"lazy\" src=\"https:\/\/people.usd.ac.id\/~ydkristanto\/wp-content\/uploads\/2026\/10\/displacement-time-graph.png\" alt=\"\" class=\"wp-image-2348\" width=\"360\" height=\"360\"\/><figcaption>Figure 1: Graph of the object&#8217;s displacement over time<\/figcaption><\/figure>\n\n\n\n<ul><li>With these parameter settings, the object is outside the animation window, so you cannot see where it is while the animation is playing. Using the graph in <a href=\"#figure1\">Figure 1<\/a>, can you determine where the object is at each moment in time? Explain how you know.<\/li><li>Based on the graph, the person claims that the object will not move back down the incline. Do you agree? If you agree, which parameter(s) would you need to change to make the object move back down the incline? Why?<\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-style-twentytwentyone-border\"><div class=\"wp-block-group__inner-container\">\n<div class=\"related-topics\">\n  <h3>Explore related topics<\/h3>\n  <p>Discover more contents with related topics in this website.<\/p>\n  <ul class=\"topics-list\">\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Mathematics\">Mathematics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Physics\">Physics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Mechanics\">Mechanics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Kinematics\">Kinematics<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Two+Dimensional+Motion\">Two-Dimensional Motion<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Inclined+Plane\">Inclined Plane<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Friction\">Friction<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Graphs\">Graphs<\/a><\/li>\n    <li><a href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/?s=Interactive+Learning+Resource\">Interactive Learning Resource<\/a><\/li>\n  <\/ul>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>What affects the motion of an object on an inclined plane? What happens when you change its initial velocity, friction, or the angle of inclination? Explore the simulation to investigate how different conditions affect the object&#8217;s motion as represented by the graph of its displacement over time. Seeing the Motion Through Graph Adjust the parameters,&hellip; <a class=\"more-link\" href=\"https:\/\/people.usd.ac.id\/~ydkristanto\/index.php\/learning-resources\/exploring-motion-on-an-inclined-plane\/\">Continue reading <span class=\"screen-reader-text\">Exploring Motion on an Inclined Plane<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":2330,"parent":1140,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exploring Motion on an Inclined Plane<\/title>\n<meta name=\"description\" content=\"Interactively explore motion on an inclined plane and connect the object&#039;s motion with its displacement-time graph.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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