{"id":424,"date":"2023-06-18T16:35:56","date_gmt":"2023-06-18T16:35:56","guid":{"rendered":"https:\/\/physigeek.com\/tr\/fiziksel-istasyon\/"},"modified":"2023-06-18T16:35:56","modified_gmt":"2023-06-18T16:35:56","slug":"fiziksel-istasyon","status":"publish","type":"post","link":"https:\/\/physigeek.com\/tr\/fiziksel-istasyon\/","title":{"rendered":"Pozisyon (fiziksel)"},"content":{"rendered":"<p>Bu makale fizikte pozisyonun ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece konumun fizikteki anlam\u0131n\u0131, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve konumun di\u011fer fizik kavramlar\u0131yla ili\u015fkisini \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-posicion-en-fisica\"><\/span> Fizikte konum nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Fizikte bir cismin veya par\u00e7ac\u0131\u011f\u0131n <strong>konumu<\/strong> , belirli bir zamanda bulundu\u011fu yerdir. Yani fizikte bir cismin konumu, bir cismin koordinat sisteminde yerini belirlemek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Ek olarak fizikte konum, bir cismin hareketini tan\u0131mlamak i\u00e7in kullan\u0131l\u0131r. Bir cismin konumu bir koordinat sistemi ile temsil edilerek konumu say\u0131larla tan\u0131mlan\u0131r ve dolay\u0131s\u0131yla cismin konumundaki de\u011fi\u015fiklik tan\u0131mlanabilir.<\/p>\n<p> Yani fizikte bir cismin konumu, konum vekt\u00f6r\u00fc ad\u0131 verilen bir vekt\u00f6rle temsil edilir. Bir sonraki b\u00f6l\u00fcmde konum vekt\u00f6r\u00fcn\u00fcn nelerden olu\u015ftu\u011funu g\u00f6rece\u011fiz.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Vector-de-posicion\"><\/span> Vekt\u00f6r pozisyonu<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Konum vekt\u00f6r\u00fc<\/strong> veya basit\u00e7e <strong>konum vekt\u00f6r\u00fc<\/strong> , bir referans sistemindeki bir noktan\u0131n konumunu tan\u0131mlayan bir vekt\u00f6rd\u00fcr; yani konum vekt\u00f6r\u00fc, bir noktan\u0131n koordinat sistemindeki konumunu belirtmek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Matematiksel olarak bir noktan\u0131n konum vekt\u00f6r\u00fc, koordinatlar\u0131n orijininden o noktaya giden vekt\u00f6r olarak tan\u0131mlan\u0131r. Bu nedenle bir noktan\u0131n konum vekt\u00f6r\u00fc, o noktan\u0131n koordinatlar\u0131ndan orijin koordinatlar\u0131n\u0131n \u00e7\u0131kar\u0131lmas\u0131yla hesaplan\u0131r. Dolay\u0131s\u0131yla konum vekt\u00f6r\u00fcn\u00fcn form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-227dd77db327b76f3f47e99a5d56c3e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r}=PO\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fda1e51b12ba3624074fcbebad72b1fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> konum vekt\u00f6r\u00fcn\u00fcn hesapland\u0131\u011f\u0131 noktad\u0131r ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-5fd89de58d79b25e5ca6ae69a6ff464b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"O\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> referans sisteminin koordinatlar\u0131n\u0131n k\u00f6kenidir.<\/p>\n<p> Bir noktan\u0131n konum vekt\u00f6r\u00fcn\u00fcn koordinatlar\u0131 birim vekt\u00f6rlerle ifade edilir<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-0b35266aff72392f18054a3ee0726b72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{i}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e64160920c9450edf06e8f621fe04ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{j}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> Ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-c04df108648dbd0ef793690ce20b8b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{k}[ \/latex], qui repr\u00e9sentent respectivement les directions des axes OX, OY et OZ. [latex]\\vv{r}=x\\vv{i}+y\\vv{j}+z\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"674\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u00d6rne\u011fin bir noktan\u0131n Kartezyen koordinatlar\u0131 (3,4,5) ise bu noktan\u0131n konum vekt\u00f6r\u00fc r=3i+4j+5k olur. <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position.png\" alt=\"konum vekt\u00f6r\u00fc \u00f6rne\u011fi\" class=\"wp-image-7644\" width=\"374\" height=\"308\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position-300x247.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position.png 697w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<p> \u00d6nceki \u00f6rnekte de g\u00f6rebilece\u011finiz gibi konum vekt\u00f6r\u00fcn\u00fcn y\u00f6n\u00fc referans sisteminin orijinini s\u00f6z konusu noktaya ba\u011flayan \u00e7izgidir ve di\u011fer taraftan konum vekt\u00f6r\u00fcn\u00fcn y\u00f6n\u00fc orijinden noktaya gider. s\u00f6z konusu. \u00e7al\u0131\u015fman\u0131n noktas\u0131.<\/p>\n<p> Bir noktan\u0131n konum vekt\u00f6r\u00fcn\u00fcn b\u00fcy\u00fckl\u00fc\u011f\u00fc, nokta ile koordinatlar\u0131n orijini aras\u0131ndaki mesafedir. Dolay\u0131s\u0131yla konum vekt\u00f6r\u00fcn\u00fcn normu, koordinatlar\u0131n\u0131n karelerinin toplam\u0131n\u0131n karek\u00f6k\u00fcne e\u015fittir.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-4e00e2651473f9b281caa2edb84af61b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{r}|=\\sqrt{x^2+y^2+z^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"153\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> D\u00fczlemde \u00e7al\u0131\u015f\u0131yorsak konum vekt\u00f6r\u00fcn\u00fcn yaln\u0131zca iki koordinata (x,y) sahip olaca\u011f\u0131n\u0131 unutmay\u0131n. \u00d6te yandan uzayda \u00e7al\u0131\u015f\u0131yorsak konum vekt\u00f6r\u00fcn\u00fcn \u00fc\u00e7 koordinat\u0131 (x,y,z) olacakt\u0131r. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/physigeek.com\/tr\">Konum vekt\u00f6r\u00fc hesaplama \u00f6rne\u011fi<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Posicion-y-desplazamiento\"><\/span> konum ve ofset<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bu b\u00f6l\u00fcmde fizikte yer de\u011fi\u015ftirmenin ne oldu\u011funu ve bunun bir cismin konumuyla nas\u0131l ili\u015fkili oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<p> Fizikte <strong>yer de\u011fi\u015ftirme<\/strong> , bir cismin veya nesnenin konumundaki de\u011fi\u015fikli\u011fi ifade eder. Ba\u015fka bir deyi\u015fle, bir cismin yer de\u011fi\u015ftirmesi, son konumu eksi ba\u015flang\u0131\u00e7 konumu \u00e7\u0131kar\u0131larak hesaplan\u0131r. Bu nedenle yer de\u011fi\u015ftirmeyi hesaplamak i\u00e7in kullan\u0131lan form\u00fcl a\u015fa\u011f\u0131daki gibidir:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-5d3939f1528e9a354c39bc01ca2925a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta \\vv{r}=\\vv{r_f}-\\vv{r_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"98\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-bd163374155626fffded43e0d746c686_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta \\vv{r}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\"><\/p>\n<p> konum vekt\u00f6r\u00fcn\u00fcn uzakl\u0131\u011f\u0131d\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e1b02810b572e656acf95dc5bb7f0c9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r_f}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -6px;\"><\/p>\n<p> son konumun konum vekt\u00f6r\u00fcd\u00fcr. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7eae0c03c02ab63fa29f02150a8bedf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"><\/p>\n<p> ba\u015flang\u0131\u00e7 konumunun konum vekt\u00f6r\u00fcd\u00fcr. <\/span><\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/physigeek.com\/tr\/fiziksel-hareket\/\">Yer de\u011fi\u015ftirme nedir? (fiziksel)<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Posicion-y-distancia\"><\/span> Konum ve mesafe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Fizikte <strong>iki nokta aras\u0131ndaki mesafe<\/strong> , noktalar\u0131 birle\u015ftiren vekt\u00f6r\u00fcn normudur. Dolay\u0131s\u0131yla yer de\u011fi\u015ftirme vekt\u00f6r\u00fc iki farkl\u0131 konumu birle\u015ftiren vekt\u00f6r oldu\u011fundan iki nokta aras\u0131ndaki uzakl\u0131k, noktalar aras\u0131ndaki yer de\u011fi\u015ftirme vekt\u00f6r\u00fcn\u00fcn b\u00fcy\u00fckl\u00fc\u011f\u00fc hesaplanarak belirlenebilir.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-75dc5dcfde010c68a3d5e0d59fc3f5b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d_{AB}=|\\Delta \\vv{r}_{AB}|=\\sqrt{(x_B-x_A)^2+(y_B-y_A)^2(z_B-z_A)^2}[\/ latex] O\u00f9:\n\n<ul style=&quot;color:#4fd12f; font-weight: bold;&quot;>\n<li style=&quot;margin-bottom:5px&quot;> <span style=&quot;color:#101010;font-weight: normal;&quot;>[latex]d_{AB}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;87&#8243; width=&#8221;582&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<p> A noktas\u0131 ile B noktas\u0131 aras\u0131ndaki mesafedir. <\/p>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7d2e05edcc86b6c52046c42e1ef45b04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta \\vv{r}_{AB}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"44\" style=\"vertical-align: -3px;\"><\/p>\n<p> A noktas\u0131 ile B noktas\u0131 aras\u0131ndaki yer de\u011fi\u015ftirme vekt\u00f6r\u00fcd\u00fcr. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-c6ccb392fef5508c79e5ce51ef6c7baf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_A, y_A, z_A\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"75\" style=\"vertical-align: -4px;\"><\/p>\n<p> A noktas\u0131n\u0131n X, Y ve Z koordinatlar\u0131d\u0131r. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-b425d4bb21c7a8701dd00fec1c581455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_B, y_B, z_B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"77\" style=\"vertical-align: -4px;\"><\/p>\n<p> B noktas\u0131n\u0131n X, Y ve Z koordinatlar\u0131d\u0131r.<\/span><\/li>\n<p> Ancak iki nokta aras\u0131ndaki mesafe kavram\u0131 ile kat edilen mesafe kavram\u0131n\u0131n farkl\u0131 mesafeler olmas\u0131 nedeniyle farkl\u0131la\u015ft\u0131r\u0131lmas\u0131 gerekir.<\/p>\n<p> <strong>Kat edilen mesafe,<\/strong> bir bedenin bir noktadan di\u011ferine gitmek i\u00e7in kat etti\u011fi uzunlu\u011fu ifade eder; yani kat edilen mesafe, v\u00fccut taraf\u0131ndan kat edilen yolun tamam\u0131d\u0131r. <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/deplacement-et-distance.png\" alt=\"Kat edilen mesafe ve yer de\u011fi\u015ftirme\" class=\"wp-image-7836\" width=\"280\" height=\"219\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/deplacement-et-distance-300x234.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/deplacement-et-distance.png 424w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<p> Bu nedenle, <strong>kat edilen mesafe ile iki nokta aras\u0131ndaki mesafe aras\u0131ndaki fark,<\/strong> kat edilen mesafenin kat edilen t\u00fcm yolun uzunlu\u011fu olmas\u0131, iki nokta aras\u0131ndaki mesafenin ise son konum ile ba\u015flang\u0131\u00e7 konumu aras\u0131ndaki mesafe olmas\u0131d\u0131r; bu da \u015funa e\u015fde\u011ferdir: yer de\u011fi\u015ftirme mod\u00fcl\u00fc. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/physigeek.com\/tr\/fiziksel-mesafe\/\">Fizikte mesafe nedir?<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Posicion-y-velocidad\"><\/span> Konum ve h\u0131z<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak, bir cismin h\u0131z\u0131 konum denkleminden hesaplanabildi\u011finden, bir cismin konumu ile h\u0131z\u0131 aras\u0131ndaki ili\u015fkinin ne oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<p> Yukar\u0131da g\u00f6rd\u00fc\u011f\u00fcm\u00fcz gibi konum vekt\u00f6r\u00fc bize bir cismin belirli bir andaki koordinatlar\u0131n\u0131 s\u00f6yleyen bir vekt\u00f6rd\u00fcr.<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-f75044a0a175ed54f5513df2e91b2573_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r}=x\\vv{i}+y\\vv{j}+z\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"127\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Bir cismin anl\u0131k konumunun zaman\u0131n bir fonksiyonu olarak denklemi, bir cismin herhangi bir andaki konumunu belirlememizi sa\u011flayan bir form\u00fcld\u00fcr:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7963fb834241aded239d9fa4e4fff290_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r}(t)=x(t)\\vv{i}+y(t)\\vv{j}+z(t)\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla bir cismin anl\u0131k h\u0131z\u0131na ili\u015fkin denklem, anl\u0131k konum denkleminin zamana g\u00f6re t\u00fcrevine e\u015fittir:<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\begin{aligned}\\vv{v}(t)&amp;=\\cfrac{d\\vv{r}(t)}{dt}\\\\[2ex]\\vv{v}(t)&amp;=\\ cfrac{dx (t)}{dt}\\vv{i}+\\cfrac{dy(t)}{dt}\\vv{j}+\\cfrac{dz(t)}{dt}\\vv{k}\\ end{aligned }\n\n*** Error message:\nPackage amsmath Error: \\begin{aligned} allowed only in math mode.\nleading text: \\begin{aligned}\\vv\nMissing $ inserted.\nleading text: \\begin{aligned}\\vv\nUndefined control sequence \\vv.\nleading text: \\begin{aligned}\\vv\nPlease use \\mathaccent for accents in math mode.\nleading text: ...\\vv{j}+\\cfrac{dz(t)}{dt}\\vv{k}\\ end{aligned\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing { inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\n\\begin{aligned} on input line 8 ended by \\end{document}.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\n\n<\/pre>\n<p> Bu nedenle, bir cismin belirli bir zamandaki anl\u0131k h\u0131z\u0131n\u0131 hesaplamak i\u00e7in, \u00f6nce cismin konumunun denklemini t\u00fcretmeli, sonra da zaman an\u0131n\u0131n de\u011ferini elde edilen ifadeye koymal\u0131y\u0131z. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/physigeek.com\/tr\">H\u0131z t\u00fcrleri<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale fizikte pozisyonun ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece konumun fizikteki anlam\u0131n\u0131, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve konumun di\u011fer fizik kavramlar\u0131yla ili\u015fkisini \u00f6\u011freneceksiniz. Fizikte konum nedir? Fizikte bir cismin veya par\u00e7ac\u0131\u011f\u0131n konumu , belirli bir zamanda bulundu\u011fu yerdir. Yani fizikte bir cismin konumu, bir cismin koordinat sisteminde yerini belirlemek i\u00e7in kullan\u0131l\u0131r. Ek olarak fizikte konum, bir cismin hareketini &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/tr\/fiziksel-istasyon\/\"> <span class=\"screen-reader-text\">Pozisyon (fiziksel)<\/span> Devam\u0131 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-424","post","type-post","status-publish","format-standard","hentry","category-sinematik"],"yoast_head":"<!-- This site is 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