{"id":436,"date":"2023-06-18T04:55:14","date_gmt":"2023-06-18T04:55:14","guid":{"rendered":"https:\/\/physigeek.com\/nl\/vectorrol\/"},"modified":"2023-06-18T04:55:14","modified_gmt":"2023-06-18T04:55:14","slug":"vectorrol","status":"publish","type":"post","link":"https:\/\/physigeek.com\/nl\/vectorrol\/","title":{"rendered":"Vectorrol"},"content":{"rendered":"<p>Dit artikel legt uit wat de verplaatsingsvector in de natuurkunde is. U zult dus ontdekken hoe u de verplaatsingsvector kunt berekenen en bovendien een opgeloste oefening om het concept goed te assimileren. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-vector-desplazamiento\"><\/span> Wat is de verplaatsingsvector?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De <strong>verplaatsingsvector<\/strong> wordt gedefinieerd als de vector die van de beginpositie naar de eindpositie gaat, dat wil zeggen dat de verplaatsingsvector de vector is die de variatie van de positie van een lichaam vertegenwoordigt. De verplaatsingsvector wordt berekend door de eindpositievector minus de initi\u00eble positievector af te trekken.<\/p>\n<p> Het toepassingspunt van de verplaatsingsvector is het punt dat de beginpositie van het lichaam definieert, terwijl het einde van de verplaatsingsvector het punt is dat de eindpositie van het lichaam aangeeft. In de natuurkunde is de verplaatsingsvector dus de vector die het verschil markeert tussen de beginpositie en de eindpositie van een lichaam.<\/p>\n<p> Het verplaatsingsvectorsymbool is<\/p>\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> . <\/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-et-de-deplacement.png\" alt=\"vectorverplaatsing\" class=\"wp-image-7663\" width=\"371\" height=\"300\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position-et-de-deplacement-300x243.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/vecteur-de-position-et-de-deplacement.png 650w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<p> Merk op dat verplaatsing iets anders is dan traject. Het traject is het gehele pad dat het mobiele lichaam aflegt, terwijl de verplaatsingsvector alleen de variatie tussen de beginpositie en de eindpositie aangeeft. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-del-vector-desplazamiento\"><\/span> Verplaatsingsvectorformule<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De verplaatsingsvector is gelijk aan het verschil tussen de eindpositievector ( <sub>rf<\/sub> ) en de initi\u00eble positievector (ri <sub>)<\/sub> . Daarom wordt de verplaatsingsvector berekend door de eindpositievector minus de initi\u00eble positievector (\u0394r = <sub>rf<\/sub> <sub>-ri<\/sub> ) af te trekken.<\/p>\n<p> De <strong>formule voor het berekenen van de verplaatsingsvector<\/strong> is daarom als volgt:<\/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-6a2add39f8b17932976b2dac8782b1e3_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> Houd er rekening mee dat als we in een systeem met twee co\u00f6rdinaten werken, elke positievector twee componenten heeft. Om het aftrekken van twee vectoren te berekenen, moeten we dus hun co\u00f6rdinaten aftrekken:<\/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-9de158fd25fcb5e34f8c8a8b2ea945ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\Delta\\vv{r}&amp;=\\vv{r_f}-\\vv{r_i}\\\\[3ex]\\Delta\\vv{r}&amp;=\\left(x_f\\vv{i }+y_f\\vv{j}\\right)-\\left(x_i\\vv{i}+y_i\\vv{j}\\right)\\\\[3ex]\\Delta\\vv{r}&amp;=(x_f-x_i) \\vv{i}+(y_f-y_i)\\vv{j}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"118\" width=\"234\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Goud: <\/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> is de verplaatsingsvector. <\/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> is de positievector op het laatste moment. <\/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> is de positievector op het beginmoment. <\/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-0d89a653d05691dbd9879857c51d283e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_f, y_f\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"44\" style=\"vertical-align: -6px;\"><\/p>\n<p> zijn respectievelijk de X- en Y-co\u00f6rdinaten van de eindpositie. <\/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-ca29b189039d3158599e42d540a4ff86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i, y_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"38\" style=\"vertical-align: -4px;\"><\/p>\n<p> zijn respectievelijk de X- en Y-co\u00f6rdinaten van de beginpositie. <\/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-38c9c3651baee200e255572b4c746a19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{i},\\vv{j}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"22\" style=\"vertical-align: -4px;\"><\/p>\n<p> zijn de eenheidsvectoren die respectievelijk de richtingen van de OX- en OY-assen vertegenwoordigen.<\/span><\/li>\n<\/ul>\n<p> <strong>Let op:<\/strong> als we in de ruimte werken, hebben de vectoren drie co\u00f6rdinaten. In dit geval moet de Z-co\u00f6rdinaat van de vectoren aan de formule worden toegevoegd en met drie co\u00f6rdinaten worden gewerkt.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Modulo-del-vector-desplazamiento\"><\/span> Modulus van de verplaatsingsvector<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> De <strong>grootte van de verplaatsingsvector<\/strong> is de afstand tussen de eindpositie en de beginpositie. Om de afstand tussen twee punten te bepalen, is het daarom noodzakelijk om de verplaatsingsmodulus tussen deze twee punten te berekenen.<\/p>\n<p> De norm van de verplaatsingsvector is gelijk aan de vierkantswortel van de som van de kwadraten van zijn componenten. De <strong>formule voor het berekenen van de modulus van de verplaatsingsvector<\/strong> is dus als volgt:<\/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-93d32dbcb616220d740d06d08ccf47ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\Delta \\vv{r}|=\\sqrt{(x_f-x_i)^2+(y_f-y_i)^2\\vphantom{\\bigl)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"247\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Goud: <\/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-e90c82c4757170808470067b919325da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\Delta \\vv{r}|\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"29\" style=\"vertical-align: -5px;\"><\/p>\n<p> is de norm van de verplaatsingsvector. <\/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-0d89a653d05691dbd9879857c51d283e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_f, y_f\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"44\" style=\"vertical-align: -6px;\"><\/p>\n<p> zijn respectievelijk de X- en Y-co\u00f6rdinaten van de eindpositie. <\/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-ca29b189039d3158599e42d540a4ff86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i, y_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"38\" style=\"vertical-align: -4px;\"><\/p>\n<p> zijn respectievelijk de X- en Y-co\u00f6rdinaten van de beginpositie.<\/span><\/li>\n<\/ul>\n<p> Houd er rekening mee dat de afstand tussen twee punten, wat de grootte is van de verplaatsingsvector tussen die punten, niet hetzelfde is als de afgelegde afstand, aangezien de afgelegde afstand groter kan zijn dan de werkelijke afstand tussen de twee punten. <\/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>Zie:<\/strong> <a href=\"https:\/\/physigeek.com\/nl\/afstand-en-offset\/\">Wat is het verschil tussen verplaatsing en afgelegde afstand?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-del-calculo-del-vector-desplazamiento\"><\/span> Voorbeeld van het berekenen van de verplaatsingsvector<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Zodra we de definitie van de verplaatsingsvector hebben gezien en wat de formule ervan is, zullen we in deze sectie zien hoe de verplaatsingsvector wordt berekend met een voorbeeld dat stap voor stap wordt opgelost.<\/p>\n<ul>\n<li> Er bevindt zich een deeltje in de positie\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-281bd088d419c8ace9624f2ac70173ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r_i}=3\\vv{i}-2\\vv{j}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\"><\/p>\n<p> op het eerste moment en na een tijdsinterval bevindt het zich in de positie <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/physigeek.com\/nl\/wp-content\/ql-cache\/quicklatex.com-7e4e6c2ebe0a7401013ac434c3437d1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#118;&#123;&#114;&#95;&#102;&#125;&#61;&#53;&#92;&#118;&#118;&#123;&#105;&#125;&#43;&#49;&#92;&#118;&#118;&#123;&#106;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -6px;\"\/>. Wat is de verplaatsingsvector en de afstand tussen deze twee posities?<\/li>\n<\/ul>\n<p> Om de verplaatsingsvector tussen de eindpositie en de beginpositie te bepalen, trekt u eenvoudigweg de twee positievectoren af:<\/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-3444222027ce5b4d04745c6beaa286f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\Delta\\vv{r}&amp;=\\vv{r_f}-\\vv{r_i}\\\\[3ex]\\Delta\\vv{r}&amp;=\\left(5\\vv{i }+1\\vv{j}\\right)-\\left(3\\vv{i}-2\\vv{j}\\right)\\\\[3ex]\\Delta\\vv{r}&amp;=\\bigl(5- 3\\bigr)\\vv{i}+\\bigl(1-(-2)\\bigr)\\vv{j}\\\\[3ex]\\Delta\\vv{r}&amp;=2\\vv{i}+3\\ vv{j}\\end{align\u00e9}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"221\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Om vervolgens de afstand tussen deze twee punten te vinden, moeten we de norm van de berekende verplaatsingsvector nemen: <\/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-e1bf43dbb25c4179e4c8a79fddb56285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}|\\Delta \\vv{r}|&amp;=\\sqrt{2^2+3^2}}\\\\[3ex]|\\Delta \\vv{r}|&amp;=\\sqrt{ 4+9}\\\\[3ex]|\\Delta \\vv{r}|&amp;=\\sqrt{13}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Vector-desplazamiento-y-vector-de-posicion\"><\/span> Verplaatsingsvector en positievector<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ten slotte zullen we zien wat het verschil is tussen de verplaatsingsvector en de positievector, en ook wat de relatie is tussen deze twee soorten vectoren.<\/p>\n<p> De <strong>positievector<\/strong> , ook wel <strong>positievector<\/strong> genoemd, is een vector die de positie van een punt ten opzichte van een referentiesysteem beschrijft. In de natuurkunde wordt de positievector dus gebruikt om de positie van een punt in een co\u00f6rdinatensysteem aan te geven.<\/p>\n<p> Bijgevolg <strong>zijn de verplaatsingsvector en de positievector met elkaar verbonden<\/strong> , aangezien de positievector de positie van een punt definieert en anderzijds de verplaatsingsvector de variatie van de positievector tussen twee tijdstippen aangeeft. <\/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>Zie:<\/strong> <a href=\"https:\/\/physigeek.com\/nl\/positievector\/\">Wat is de positievector?<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Dit artikel legt uit wat de verplaatsingsvector in de natuurkunde is. U zult dus ontdekken hoe u de verplaatsingsvector kunt berekenen en bovendien een opgeloste oefening om het concept goed te assimileren. Wat is de verplaatsingsvector? De verplaatsingsvector wordt gedefinieerd als de vector die van de beginpositie naar de eindpositie gaat, dat wil zeggen dat &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/nl\/vectorrol\/\"> <span class=\"screen-reader-text\">Vectorrol<\/span> Weiterlesen &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-436","post","type-post","status-publish","format-standard","hentry","category-filmisch"],"yoast_head":"<!-- This site is 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