Willard Roseberry's List: Game Math consepts

<h4><a rel="nofollow" name="tth_sEc4.2" href="" id="tth_sEc4.2">4.2</a><br/>Physics</h4><br/><div>Every object has a <span style="font-style: italic;">position</span> , which is a vector<br/><span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-85-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-592" class="math"><span style="display: inline-block; position: relative; width: 0.621em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(2.193em 1000em 2.976em -0.487em); top: -2.807em; left: 0em;"><span id="MathJax-Span-593" class="mrow"><span id="MathJax-Span-594" class="texatom"><span id="MathJax-Span-595" class="mrow"><span id="MathJax-Span-596" class="mi" style="font-family: MathJax_Main; font-weight: bold;">x</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.685em; vertical-align: -0.069em;"></span></span></nobr></span>. It also has a <span style="font-style: italic;">velocity</span> , which is the direction it<br/>is travelling in, it is also a vector <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-86-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-597" class="math"><span style="display: inline-block; position: relative; width: 0.621em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(2.193em 1000em 2.979em -0.482em); top: -2.807em; left: 0em;"><span id="MathJax-Span-598" class="mrow"><span id="MathJax-Span-599" class="texatom"><span id="MathJax-Span-600" class="mrow"><span id="MathJax-Span-601" class="mi" style="font-family: MathJax_Main; font-weight: bold;">v</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.689em; vertical-align: -0.073em;"></span></span></nobr></span>, sometimes<br/>written as <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-87-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-602" class="math"><span style="display: inline-block; position: relative; width: 0.621em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(3.075em 1000em 4.169em -0.487em); top: -4em; left: 0em;"><span id="MathJax-Span-603" class="mrow"><span id="MathJax-Span-604" class="texatom"><span id="MathJax-Span-605" class="mrow"><span id="MathJax-Span-606" class="texatom"><span id="MathJax-Span-607" class="mrow"><span id="MathJax-Span-608" class="munderover"><span style="display: inline-block; position: relative; width: 0.621em; height: 0px;"><span style="position: absolute; clip: rect(2.193em 1000em 2.976em -0.487em); top: -2.807em; left: 0em;"><span id="MathJax-Span-609" class="mi" style="font-family: MathJax_Main; font-weight: bold;">x</span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span><span style="position: absolute; clip: rect(1.942em 1000em 2.451em -0.306em); top: -2.867em; left: 0.028em;"><span id="MathJax-Span-610" class="mo" style="font-family: MathJax_Main; font-weight: bold;">˙</span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 1.068em; vertical-align: -0.069em;"></span></span></nobr></span>. Every object also has something<br/>called an <span style="font-style: italic;">acceleration</span> ,<br/>this is how fast the velocity is changing, and it is also a vector<br/><span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-88-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-611" class="math"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(2.184em 1000em 2.982em -0.476em); top: -2.807em; left: 0em;"><span id="MathJax-Span-612" class="mrow"><span id="MathJax-Span-613" class="texatom"><span id="MathJax-Span-614" class="mrow"><span id="MathJax-Span-615" class="mi" style="font-family: MathJax_Main; font-weight: bold;">a</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.703em; vertical-align: -0.077em;"></span></span></nobr></span>, sometimes written as <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-89-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-616" class="math"><span style="display: inline-block; position: relative; width: 0.621em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(3.085em 1000em 4.169em -0.487em); top: -4em; left: 0em;"><span id="MathJax-Span-617" class="mrow"><span id="MathJax-Span-618" class="texatom"><span id="MathJax-Span-619" class="mrow"><span id="MathJax-Span-620" class="texatom"><span id="MathJax-Span-621" class="mrow"><span id="MathJax-Span-622" class="munderover"><span style="display: inline-block; position: relative; width: 0.621em; height: 0px;"><span style="position: absolute; clip: rect(2.193em 1000em 2.976em -0.487em); top: -2.807em; left: 0em;"><span id="MathJax-Span-623" class="mi" style="font-family: MathJax_Main; font-weight: bold;">x</span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span><span style="position: absolute; clip: rect(1.942em 1000em 2.441em -0.412em); top: -2.857em; left: 0.028em;"><span id="MathJax-Span-624" class="mo" style="font-family: MathJax_Main; font-weight: bold;">¨</span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 1.055em; vertical-align: -0.069em;"></span></span></nobr></span>. Finally,<br/>every object has something called <span style="font-style: italic;">mass</span> , this is basically how heavy the<br/>object is, and is usually written <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-90-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-625" class="math"><span style="display: inline-block; position: relative; width: 0.903em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(1.969em 1000em 2.761em -0.487em); top: -2.581em; left: 0em;"><span id="MathJax-Span-626" class="mrow"><span id="MathJax-Span-627" class="mi" style="font-family: MathJax_Math; font-style: italic;">m</span></span><span style="display: inline-block; width: 0px; height: 2.581em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.696em; vertical-align: -0.083em;"></span></span></nobr></span>, but this is not a vector. If<br/>an object starts at position <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-91-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-628" class="math"><span style="display: inline-block; position: relative; width: 0.621em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(2.193em 1000em 2.976em -0.487em); top: -2.807em; left: 0em;"><span id="MathJax-Span-629" class="mrow"><span id="MathJax-Span-630" class="texatom"><span id="MathJax-Span-631" class="mrow"><span id="MathJax-Span-632" class="mi" style="font-family: MathJax_Main; font-weight: bold;">x</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.685em; vertical-align: -0.069em;"></span></span></nobr></span>, and has a velocity<br/><span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-92-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-633" class="math"><span style="display: inline-block; position: relative; width: 0.621em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(2.193em 1000em 2.979em -0.482em); top: -2.807em; left: 0em;"><span id="MathJax-Span-634" class="mrow"><span id="MathJax-Span-635" class="texatom"><span id="MathJax-Span-636" class="mrow"><span id="MathJax-Span-637" class="mi" style="font-family: MathJax_Main; font-weight: bold;">v</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.689em; vertical-align: -0.073em;"></span></span></nobr></span> which doesn't change, then after <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-93-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-638" class="math"><span style="display: inline-block; position: relative; width: 0.339em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(1.785em 1000em 2.761em -0.489em); top: -2.581em; left: 0em;"><span id="MathJax-Span-639" class="mrow"><span id="MathJax-Span-640" class="mi" style="font-family: MathJax_Math; font-style: italic;">t</span></span><span style="display: inline-block; width: 0px; height: 2.581em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.922em; vertical-align: -0.083em;"></span></span></nobr></span> seconds, the<br/>position of the object is <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-94-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-641" class="math"><span style="display: inline-block; position: relative; width: 6.098em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(2.011em 1000em 3.134em -0.487em); top: -2.807em; left: 0em;"><span id="MathJax-Span-642" class="mrow"><span id="MathJax-Span-643" class="msubsup"><span style="display: inline-block; position: relative; width: 0.978em; height: 0px;"><span style="position: absolute; clip: rect(2.193em 1000em 2.976em -0.487em); top: -2.807em; left: 0em;"><span id="MathJax-Span-644" class="texatom"><span id="MathJax-Span-645" class="mrow"><span id="MathJax-Span-646" class="mi" style="font-family: MathJax_Main; font-weight: bold;">x</span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span><span style="position: absolute; top: -2.205em; left: 0.621em;"><span id="MathJax-Span-647" class="mi" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 2.355em;"></span></span></span></span><span id="MathJax-Span-648" class="mo" style="font-family: MathJax_Main; padding-left: 0.278em;">=</span><span id="MathJax-Span-649" class="texatom" style="padding-left: 0.278em;"><span id="MathJax-Span-650" class="mrow"><span id="MathJax-Span-651" class="mi" style="font-family: MathJax_Main; font-weight: bold;">x</span></span></span><span id="MathJax-Span-652" class="mo" style="font-family: MathJax_Main; padding-left: 0.222em;">+</span><span id="MathJax-Span-653" class="texatom" style="padding-left: 0.222em;"><span id="MathJax-Span-654" class="mrow"><span id="MathJax-Span-655" class="mi" style="font-family: MathJax_Main; font-weight: bold;">v</span></span></span><span id="MathJax-Span-656" class="mo" style="font-family: MathJax_Main; padding-left: 0.222em;">×</span><span id="MathJax-Span-657" class="mi" style="font-family: MathJax_Math; font-style: italic; padding-left: 0.222em;">t</span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 1.103em; vertical-align: -0.264em;"></span></span></nobr></span>. In case you're wondering what <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-95-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-658" class="math"><span style="display: inline-block; position: relative; width: 0.978em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(3.387em 1000em 4.327em -0.487em); top: -4em; left: 0em;"><span id="MathJax-Span-659" class="mrow"><span id="MathJax-Span-660" class="msubsup"><span style="display: inline-block; position: relative; width: 0.978em; height: 0px;"><span style="position: absolute; clip: rect(2.193em 1000em 2.976em -0.487em); top: -2.807em; left: 0em;"><span id="MathJax-Span-661" class="texatom"><span id="MathJax-Span-662" class="mrow"><span id="MathJax-Span-663" class="mi" style="font-family: MathJax_Main; font-weight: bold;">x</span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span><span style="position: absolute; top: -2.205em; left: 0.621em;"><span id="MathJax-Span-664" class="mi" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 2.355em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.879em; vertical-align: -0.264em;"></span></span></nobr></span> means, it just<br/>means the position at time <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-96-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-665" class="math"><span style="display: inline-block; position: relative; width: 0.339em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(1.785em 1000em 2.761em -0.489em); top: -2.581em; left: 0em;"><span id="MathJax-Span-666" class="mrow"><span id="MathJax-Span-667" class="mi" style="font-family: MathJax_Math; font-style: italic;">t</span></span><span style="display: inline-block; width: 0px; height: 2.581em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.922em; vertical-align: -0.083em;"></span></span></nobr></span>. Similarly, <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-97-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-668" class="math"><span style="display: inline-block; position: relative; width: 0.978em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(3.387em 1000em 4.327em -0.482em); top: -4em; left: 0em;"><span id="MathJax-Span-669" class="mrow"><span id="MathJax-Span-670" class="msubsup"><span style="display: inline-block; position: relative; width: 0.978em; height: 0px;"><span style="position: absolute; clip: rect(2.193em 1000em 2.979em -0.482em); top: -2.807em; left: 0em;"><span id="MathJax-Span-671" class="texatom"><span id="MathJax-Span-672" class="mrow"><span id="MathJax-Span-673" class="mi" style="font-family: MathJax_Main; font-weight: bold;">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span><span style="position: absolute; top: -2.205em; left: 0.621em;"><span id="MathJax-Span-674" class="mi" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 2.355em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.879em; vertical-align: -0.264em;"></span></span></nobr></span> means the<br/>velocity at time <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-98-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-675" class="math"><span style="display: inline-block; position: relative; width: 0.339em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(1.785em 1000em 2.761em -0.489em); top: -2.581em; left: 0em;"><span id="MathJax-Span-676" class="mrow"><span id="MathJax-Span-677" class="mi" style="font-family: MathJax_Math; font-style: italic;">t</span></span><span style="display: inline-block; width: 0px; height: 2.581em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.922em; vertical-align: -0.083em;"></span></span></nobr></span>. If an objects starts with velocity<br/><span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-99-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-678" class="math"><span style="display: inline-block; position: relative; width: 0.621em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(2.193em 1000em 2.979em -0.482em); top: -2.807em; left: 0em;"><span id="MathJax-Span-679" class="mrow"><span id="MathJax-Span-680" class="texatom"><span id="MathJax-Span-681" class="mrow"><span id="MathJax-Span-682" class="mi" style="font-family: MathJax_Main; font-weight: bold;">v</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.689em; vertical-align: -0.073em;"></span></span></nobr></span> and has an acceleration <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-100-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-683" class="math"><span style="display: inline-block; position: relative; width: 0.565em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(2.184em 1000em 2.982em -0.476em); top: -2.807em; left: 0em;"><span id="MathJax-Span-684" class="mrow"><span id="MathJax-Span-685" class="texatom"><span id="MathJax-Span-686" class="mrow"><span id="MathJax-Span-687" class="mi" style="font-family: MathJax_Main; font-weight: bold;">a</span></span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.703em; vertical-align: -0.077em;"></span></span></nobr></span> which doesn't<br/>change, then after <span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-101-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-688" class="math"><span style="display: inline-block; position: relative; width: 0.339em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(1.785em 1000em 2.761em -0.489em); top: -2.581em; left: 0em;"><span id="MathJax-Span-689" class="mrow"><span id="MathJax-Span-690" class="mi" style="font-family: MathJax_Math; font-style: italic;">t</span></span><span style="display: inline-block; width: 0px; height: 2.581em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 0.922em; vertical-align: -0.083em;"></span></span></nobr></span> seconds, the velocity of the object is<br/><span class="MathJax_Preview"></span><span role="textbox" aria-readonly="true" id="MathJax-Element-102-Frame" class="MathJax" style=""><nobr><span id="MathJax-Span-691" class="math"><span style="display: inline-block; position: relative; width: 6.041em; height: 0px; font-size: 123%;"><span style="position: absolute; clip: rect(2.011em 1000em 3.134em -0.482em); top: -2.807em; left: 0em;"><span id="MathJax-Span-692" class="mrow"><span id="MathJax-Span-693" class="msubsup"><span style="display: inline-block; position: relative; width: 0.978em; height: 0px;"><span style="position: absolute; clip: rect(2.193em 1000em 2.979em -0.482em); top: -2.807em; left: 0em;"><span id="MathJax-Span-694" class="texatom"><span id="MathJax-Span-695" class="mrow"><span id="MathJax-Span-696" class="mi" style="font-family: MathJax_Main; font-weight: bold;">v</span></span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span><span style="position: absolute; top: -2.205em; left: 0.621em;"><span id="MathJax-Span-697" class="mi" style="font-size: 70.7%; font-family: MathJax_Math; font-style: italic;">t</span><span style="display: inline-block; width: 0px; height: 2.355em;"></span></span></span></span><span id="MathJax-Span-698" class="mo" style="font-family: MathJax_Main; padding-left: 0.278em;">=</span><span id="MathJax-Span-699" class="texatom" style="padding-left: 0.278em;"><span id="MathJax-Span-700" class="mrow"><span id="MathJax-Span-701" class="mi" style="font-family: MathJax_Main; font-weight: bold;">v</span></span></span><span id="MathJax-Span-702" class="mo" style="font-family: MathJax_Main; padding-left: 0.222em;">+</span><span id="MathJax-Span-703" class="texatom" style="padding-left: 0.222em;"><span id="MathJax-Span-704" class="mrow"><span id="MathJax-Span-705" class="mi" style="font-family: MathJax_Main; font-weight: bold;">a</span></span></span><span id="MathJax-Span-706" class="mo" style="font-family: MathJax_Main; padding-left: 0.222em;">×</span><span id="MathJax-Span-707" class="mi" style="font-family: MathJax_Math; font-style: italic; padding-left: 0.222em;">t</span></span><span style="display: inline-block; width: 0px; height: 2.807em;"></span></span></span><span style="border-left-width: 0em; border-left-style: solid; display: inline-block; overflow: hidden; width: 0px; height: 1.103em; vertical-align: -0.264em;"></span></span></nobr></span>.</div>