{"id":16638,"date":"2023-03-16T10:34:41","date_gmt":"2023-03-16T09:34:41","guid":{"rendered":"https:\/\/college-willy-ronis.fr\/maths\/?p=16638"},"modified":"2023-03-16T10:42:34","modified_gmt":"2023-03-16T09:42:34","slug":"chapitre-16-vitesse","status":"publish","type":"post","link":"https:\/\/college-willy-ronis.fr\/maths\/chapitre-16-vitesse\/","title":{"rendered":"Chapitre 16 : Vitesse"},"content":{"rendered":"\t\t
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Chapitre 16<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Vitesse<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Chapitre 16 : Vitesse<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Lors d’un trajet en voiture, la vitesse n’est pas constante (acc\u00e9l\u00e9rations, ralentissements…). La vitesse moyenne<\/strong> est la vitesse qu’aurait cette voiture si elle parcourait la m\u00eame distance dans le m\u00eame temps en conservant toujours la m\u00eame vitesse.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Propri\u00e9t\u00e9 :<\/strong> Dire que $v$ est la vitesse moyenne lors d’un trajet signifie que la distance parcourue $d$ est proportionnelle \u00e0 la dur\u00e9e $t$ du trajet.
Le coefficient de proportionnalit\u00e9 est la vitesse moyenne $v$.<\/p>

\"\"
Ainsi :
\\[d=v\\times t\\]\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Cons\u00e9quence :<\/strong> La vitesse moyenne sur un trajet est le quotient de la distance parcourue $d$ par la dur\u00e9e $t$ du trajet.
\\[v=\\dfrac{d}{t}~~~~\\text{et}~~~~t=\\dfrac{d}{v}\\]\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Exemple :<\/strong> Calcul d’une vitesse moyenne<\/strong>
Un automobiliste a parcouru $98~\\text{km}$ en $1~\\text{h}10~\\text{min}$. Calculer sa vitesse moyenne en km\/h.<\/p>

$1~\\text{h}10~\\text{min}= 70~\\text{min}$
\\begin{eqnarray*}
v&=&\\dfrac{d}{t}\\\\
v&=&\\dfrac{98~\\text{km}}{70~\\text{min}}\\\\
v&=&1,4~\\text{km\/min}\\\\
v&=&1,4\\times 60~\\text{km\/h}\\\\
v&=&84~\\text{km\/h}
\\end{eqnarray*}
Cet automobiliste a roul\u00e9 \u00e0 une vitesse moyenne de $84~\\text{km\/h}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Exemple : Calcul d’une distance<\/strong>
Un randonneur a march\u00e9 \u00e0 une vitesse de $5,6~\\text{km\/h}$ pendant $2~\\text{h}30~\\text{min}$. Quelle distance a-t-il parcourue ?<\/p>

$2~\\text{h}30~\\text{min}=2,5~\\text{h}$<\/p>

\\begin{eqnarray*}
d&=&v\\times t\\\\
d&=&5,6~\\text{km\/h}\\times 2,5~\\text{h}\\\\
d&=&14~\\text{km}
\\end{eqnarray*}
Ce randonneur a parcouru $14~\\text{km}$ en $2~\\text{h}30~\\text{min}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Exemple : Calcul d’une dur\u00e9e<\/strong>
Un skieur parcourt une descente de ski de $1~\\text{km}$ \u00e0 la vitesse de $252~\\text{km\/h}$. Quelle est la dur\u00e9e de la descente ?<\/p>

\\begin{eqnarray*}
t&=&\\dfrac{d}{v}\\\\
t&=&\\dfrac{1~\\text{km}}{252~\\text{km\/h}}\\\\
t&\\approx &0,004~\\text{h}\\\\
t&\\approx &0,004\\times 3~600~\\text{s}\\\\
t&\\approx &14,4~\\text{s}
\\end{eqnarray*}
La dur\u00e9e de cette descente est d’environ $14,4~\\text{s}$.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\n\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t<\/i>\t\t\t<\/span>\n\t\t\t\t\t\tExercices corrig\u00e9s<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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Chapitre 16 Vitesse Chapitre 16 : Vitesse Lors d’un trajet en voiture, la vitesse n’est pas constante (acc\u00e9l\u00e9rations, ralentissements…). La vitesse moyenne est la vitesse qu’aurait cette voiture si elle parcourait la m\u00eame distance dans le m\u00eame temps en conservant toujours la m\u00eame vitesse. Propri\u00e9t\u00e9 : Dire que $v$ est la vitesse moyenne lors d’un […]<\/p>\n","protected":false},"author":7440,"featured_media":16639,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"page-builder","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":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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