{"id":39622,"date":"2024-12-24T13:19:58","date_gmt":"2024-12-24T13:19:58","guid":{"rendered":"https:\/\/idea.membrane.com\/songwriter\/?p=39622"},"modified":"2024-12-24T13:19:58","modified_gmt":"2024-12-24T13:19:58","slug":"per-second-per-second","status":"publish","type":"post","link":"http:\/\/kingarthur.com\/songwriter\/2024\/12\/24\/per-second-per-second\/","title":{"rendered":"Per Second per Second"},"content":{"rendered":"<ul>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Per-Second-per-Second-I.mp3\"> Per-Second-per-Second-I.mp3<\/a><\/li>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Per-Second-per-Second-I.mp4\"> Per-Second-per-Second-I.mp4<\/a><\/li>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Per-Second-per-Second-II.mp3\"> Per-Second-per-Second-II.mp3<\/a><\/li>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Per-Second-per-Second-II.mp4\"> Per-Second-per-Second-II.mp4<\/a><\/li>\n<li><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/Per-Second-per-Second-intro.mp3\"> Per-Second-per-Second-intro.mp3<\/a><\/li>\n<\/ul>\n<p>[Intro]<br \/>\nThirty-two feet<br \/>\n(Per second per second)<br \/>\nOh, that&#8217;s deep<br \/>\n(Square aware)<\/p>\n<p>[Verse 1]<br \/>\nWhich falls faster<br \/>\nAn egg or a rock<br \/>\nWhy at the same clock<br \/>\nThough the egg&#8217;s a disaster<\/p>\n<p>[Chorus]<br \/>\nThirty-two feet<br \/>\n(Per second per second)<br \/>\nOh, that&#8217;s deep<br \/>\n(Square aware)<\/p>\n<p>[Bridge]<br \/>\nFalling (falling fast)<br \/>\nFalling faster (as time goes past)<br \/>\n32, 64, 128<br \/>\n(An exponential rate)<\/p>\n<p>[Verse 2]<br \/>\nNow I&#8217;ve come to know<br \/>\nHow fast things go<br \/>\nThere for a second&#8230;<br \/>\nI had to reckon<\/p>\n<p>[Chorus]<br \/>\nThirty-two feet<br \/>\n(Per second per second)<br \/>\nOh, that&#8217;s deep<br \/>\n(Square aware)<\/p>\n<p>[Bridge]<br \/>\nFalling (falling fast)<br \/>\nFalling faster (as time goes past)<br \/>\n32, 64, 128<br \/>\n(An exponential rate)<\/p>\n<p>[Chorus]<br \/>\nThirty-two feet<br \/>\n(Per second per second)<br \/>\nOh, that&#8217;s deep<br \/>\n(Square aware)<\/p>\n<p>[Outro]<br \/>\nI&#8217;m aware<br \/>\n(Squared there)<\/p>\n<p>A SCIENCE NOTE<\/p>\n<h3><strong>What Does &#8220;Per Second Per Second&#8221; Mean?<\/strong><\/h3>\n<ul>\n<li>&#8220;Per second per second&#8221; refers to acceleration, the rate at which velocity changes over time. For example:\n<ul>\n<li>If an object&#8217;s velocity increases by <span class=\"katex\"><span class=\"katex-mathml\">10\u2009m\/s1 <\/span><\/span>every second, it has an acceleration of <span class=\"katex\"><span class=\"katex-mathml\">10\u2009m\/s2<\/span><\/span>.<\/li>\n<li>This is read as &#8220;meters per second squared&#8221; or &#8220;meters per second per second.&#8221;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3><strong>How Fast Does an Object Fall?<\/strong><\/h3>\n<ul>\n<li>Near the surface of the Earth, objects fall with an acceleration due to gravity, denoted by <span class=\"katex\"><span class=\"katex-mathml\">gg<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">g<\/span><\/span><\/span><\/span>, approximately <span class=\"katex\"><span class=\"katex-mathml\">9.8\u2009m\/s2<\/span><\/span> (or <span class=\"katex\"><span class=\"katex-mathml\">32\u2009ft\/s2 &#8212; 32 feet per second per second<\/span><\/span>).<\/li>\n<li>Assuming no air resistance, the speed of a falling object can be calculated using the formula:<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">v=g\u22c5t<br \/>\n<\/span><\/span><\/span>where:<\/p>\n<ul>\n<li><span class=\"katex\"><span class=\"katex-mathml\">v<\/span><\/span> is the velocity,<\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\">g=9.8\u2009m\/s2<\/span><\/span><\/li>\n<li><span class=\"katex\"><span class=\"katex-mathml\">t<\/span><\/span> is the time in seconds.<\/li>\n<\/ul>\n<p>Example:<\/p>\n<ul>\n<li>After 1 second: <span class=\"katex\"><span class=\"katex-mathml\">v=9.8\u2009m\/s \u00a0 \u00a0 v = 9.8.<\/span><\/span><\/li>\n<li>After 2 seconds: <span class=\"katex\"><span class=\"katex-mathml\">v=19.6\u2009m\/s\u00a0 v = 19.6<\/span><\/span>.<\/li>\n<li>After 3 seconds: <span class=\"katex\"><span class=\"katex-mathml\">v=29.4\u2009m\/s\u00a0 v = 29.4<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3><strong>Do Objects Fall at the Same Speed Regardless of Weight?<\/strong><\/h3>\n<ul>\n<li><strong>In the absence of air resistance<\/strong> (in a vacuum), all objects fall at the same rate regardless of their mass. This is because the force of gravity acts equally on all objects relative to their mass.\n<ul>\n<li>Example: A feather and a hammer will fall at the same rate in a vacuum (as demonstrated during the Apollo 15 moon landing).<\/li>\n<\/ul>\n<\/li>\n<li><strong>With air resistance<\/strong>, heavier or denser objects usually fall faster because they are less affected by drag. For example:\n<ul>\n<li>A bowling ball falls faster than a feather in Earth&#8217;s atmosphere due to the feather&#8217;s higher air resistance relative to its weight.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr \/>\n<h3><strong>Key Equations and Concepts<\/strong><\/h3>\n<ol>\n<li><strong>Distance Fallen Over Time<\/strong>:<span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">d=1\/2 gt2 <\/span><\/span><\/span>.<\/li>\n<li><strong>Terminal Velocity<\/strong>:\n<ul>\n<li>In real-world conditions, objects reach a maximum falling speed (terminal velocity) when air resistance balances the force of gravity.\u00a0 This is why rain does not kill you.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Galileo\u2019s Discovery<\/strong>:\n<ul>\n<li>Galileo showed that objects fall at the same rate regardless of their weight, overturning Aristotle&#8217;s earlier belief that heavier objects fall faster.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h3>From the album &#8220;<a href=\"http:\/\/idea.membrane.com\/songwriter\/tag\/oh-thats-what-you-meant\/\">Oh, That&#8217;s What You Meant<\/a>&#8221; by <a href=\"http:\/\/membrane.com\/The_Beatless_Sense_Mongers\/\">The Beatless Sense Mongers<\/a><\/h3>\n<h2><a href=\"http:\/\/membrane.com\/global_warming\/\">The Human Induced Climate Change Experiment<\/a><\/h2>\n<h2><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/IX\/\">MegaEpix Enormous<\/a><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>Per-Second-per-Second-I.mp3 Per-Second-per-Second-I.mp4 Per-Second-per-Second-II.mp3 Per-Second-per-Second-II.mp4 Per-Second-per-Second-intro.mp3 [Intro] Thirty-two feet (Per second per second) Oh, that&#8217;s deep (Square aware) [Verse 1] Which falls faster An egg or a rock Why at the same clock Though the egg&#8217;s a disaster [Chorus] Thirty-two feet (Per second per second) Oh, that&#8217;s deep (Square aware) [Bridge] Falling (falling fast) Falling faster [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[3,9,14,3955,24],"tags":[546,563,4070],"class_list":["post-39622","post","type-post","status-publish","format-standard","hentry","category-4d-music","category-daniel","category-lyrics","category-megaepix-enormous","category-the-beatless-sense-mongers","tag-mp4","tag-music-videos","tag-oh-thats-what-you-meant"],"_links":{"self":[{"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/39622","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/comments?post=39622"}],"version-history":[{"count":5,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/39622\/revisions"}],"predecessor-version":[{"id":39637,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/39622\/revisions\/39637"}],"wp:attachment":[{"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/media?parent=39622"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/categories?post=39622"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/tags?post=39622"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}