Chers finalistes, préparez-vous pour le grand jour avec nos contenus !

Des items de toutes les options taillés sur mesure pour que vous prépariez mieux vos épreuves

Start learning
Expression particulier de chute libre

Rappel

Comment fut trouvée la valeur de l’accélération de pesanteur ?

Motivation

Comment s’appelle la normalité et la molalité ?

Annonce du sujet

Qu'allons-nous étudier aujourd'hui?

Analyse

Quelle est l'expression de la chute libre?

Exemple

On lance une Balle vers le bas avec une vitesse de 10m/sec. Sachant que la Balle a été lancée à une hauteur de 10m, elle arrive au sol avec une vitesse de ?

Comment calculer la vitesse Vo ?

Synthèse

Une Balle lancée verticalement de haut passe par le point A après 3 secondes en montant et après 2 secondes  en descendant.

Calculer la vitesse initiale ?

Les valeurs furent trouvées en France comme suit :

H=4,90m, t=sec

La normalité et la molalité sont les expressions de concentration.

Aujourd'hui, nous allons étudier l'Expression particulier de chute libre.

L’expression particulière de la chute libre

Pour un objet lancé vers le bas avec une vitesse Vo verticale,

Exemple

On lance une Balle vers le bas avec une vitesse de 10m/sec. Sachant que la Balle a été lancée à une hauteur de 10m, elle arrive au sol avec une vitesse de ?

Solution

Une Balle lancée verticalement vers la hauteur passe en un point de la hauteur principale après un t1 en montant et repose après un t2 en descendant.

 

8.1.28PHP Version130msRequest Duration5MBMemory UsageGET lessons/{id}/{slug}Route
    • Booting (31.27ms)
    • Application (98.18ms)
    • 1 x Application (75.79%)
      98.18ms
      1 x Booting (24.14%)
      31.27ms
      7 templates were rendered
      • public.lessons.show (resources/views/public/lessons/show.blade.php)2bladefile
        Params
        0
        lesson
        1
        lessons
      • components.banner-page (resources/views/components/banner-page.blade.php)7bladefile
        Params
        0
        property
        1
        firstTitle
        2
        secondTitle
        3
        src
        4
        attributes
        5
        slot
        6
        __laravel_slots
      • components.ad-card-lesson-long (resources/views/components/ad-card-lesson-long.blade.php)7bladefile
        Params
        0
        summary
        1
        title
        2
        actionLink
        3
        actionText
        4
        attributes
        5
        slot
        6
        __laravel_slots
      • components.button-link (resources/views/components/button-link.blade.php)6bladefile
        Params
        0
        class
        1
        title
        2
        href
        3
        attributes
        4
        slot
        5
        __laravel_slots
      • layouts.public (resources/views/layouts/public.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        lesson
        4
        lessons
        5
        component
        6
        __currentLoopData
        7
        lesson_
        8
        loop
        9
        section
      • layouts.include.public.header (resources/views/layouts/include/public/header.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        lesson
        4
        lessons
        5
        component
        6
        __currentLoopData
        7
        lesson_
        8
        loop
        9
        section
      • layouts.include.public.footer (resources/views/layouts/include/public/footer.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        lesson
        4
        lessons
        5
        component
        6
        __currentLoopData
        7
        lesson_
        8
        loop
        9
        section
      uri
      GET lessons/{id}/{slug}
      middleware
      web
      controller
      App\Http\Controllers\Public\LessonController@show
      as
      public.lesson.show
      namespace
      prefix
      /lessons
      where
      file
      app/Http/Controllers/Public/LessonController.php:86-138
      16 statements were executed59.74ms
      • select * from `oldt_posts` where (`id` = '832' and `slug` = 'expression-particulier-de-chute-libre') and exists (select * from `oldt_material_sheets` where `oldt_posts`.`material_sheet_id` = `oldt_material_sheets`.`id`) limit 1
        3.12ms/app/Http/Controllers/Public/LessonController.php:92schoolap
        Metadata
        Bindings
        • 0. 832
        • 1. expression-particulier-de-chute-libre
        Backtrace
        • 15. /app/Http/Controllers/Public/LessonController.php:92
        • 16. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `lessons` where `lessons`.`id` = '832' and `lessons`.`deleted_at` is null limit 1
        870μs/app/Repositories/LessonRepository.php:41schoolap
        Metadata
        Bindings
        • 0. 832
        Backtrace
        • 19. /app/Repositories/LessonRepository.php:41
        • 20. /app/Http/Controllers/Public/LessonController.php:95
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `lessons` where `lessons`.`deleted_at` is null order by RAND() limit 4
        42.21ms/app/Http/Controllers/Public/LessonController.php:96schoolap
        Metadata
        Backtrace
        • 14. /app/Http/Controllers/Public/LessonController.php:96
        • 15. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 16. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • update `lessons` set `count_view` = `count_view` + 1, `lessons`.`updated_at` = '2025-05-02 00:37:03' where `id` = 832 and `lessons`.`deleted_at` is null
        5.25ms/app/Http/Controllers/Public/LessonController.php:98schoolap
        Metadata
        Bindings
        • 0. 2025-05-02 00:37:03
        • 1. 832
        Backtrace
        • 16. /app/Http/Controllers/Public/LessonController.php:98
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `chapters` where `chapters`.`id` = 419 and `chapters`.`deleted_at` is null limit 1
        760μsview::public.lessons.show:10schoolap
        Metadata
        Bindings
        • 0. 419
        Backtrace
        • 20. view::public.lessons.show:10
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `course_classes` where `course_classes`.`id` = 13 and `course_classes`.`deleted_at` is null limit 1
        570μsview::public.lessons.show:10schoolap
        Metadata
        Bindings
        • 0. 13
        Backtrace
        • 20. view::public.lessons.show:10
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `classes` where `classes`.`id` in (49) and `classes`.`deleted_at` is null
        630μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 25. view::public.lessons.show:10
        • 27. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 28. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 29. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 30. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `cycle_levels` where `cycle_levels`.`id` in (72)
        490μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 30. view::public.lessons.show:10
        • 32. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 35. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `cycles` where `cycles`.`id` in (11)
        530μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 35. view::public.lessons.show:10
        • 37. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 38. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 39. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 40. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `levels` where `levels`.`id` in (30)
        590μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 35. view::public.lessons.show:10
        • 37. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 38. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 39. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 40. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `courses` where `courses`.`id` in (16) and `courses`.`deleted_at` is null
        510μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 25. view::public.lessons.show:10
        • 27. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 28. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 29. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 30. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_sections` where `lesson_sections`.`lesson_id` = 832 and `lesson_sections`.`lesson_id` is not null
        790μsview::public.lessons.show:116schoolap
        Metadata
        Bindings
        • 0. 832
        Backtrace
        • 19. view::public.lessons.show:116
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 24. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 1796 and `lesson_contents`.`deleted_at` is null limit 1
        630μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 1796
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 1642 and `content_texts`.`deleted_at` is null limit 1
        1.14msview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 1642
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 1797 and `lesson_contents`.`deleted_at` is null limit 1
        580μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 1797
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 1643 and `content_texts`.`deleted_at` is null limit 1
        1.07msview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 1643
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      App\Models\ContentText
      2
      App\Models\Lesson\LessonContent
      2
      App\Models\Lesson\LessonSection
      2
      App\Models\Course\Course
      1
      App\Models\Level
      1
      App\Models\Cycle
      1
      App\Models\CycleLevel
      1
      App\Models\Classe
      1
      App\Models\Course\CourseClass
      1
      App\Models\Chapter
      1
      App\Models\Lesson\Lesson
      5
        _token
        C4N11f00JaKmuz1VuPi5PiEJWy6ITw2Ff8JdPuif
        applocale
        en
        _previous
        array:1 [ "url" => "https://s8.schoolap.com/lessons/832/expression-particulier-de-chute-libre" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /lessons/832/expression-particulier-de-chute-libre
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "connection" => array:1 [ 0 => "keep-alive" ] "host" => array:1 [ 0 => "s8.schoolap.com" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
        request_server
        0 of 0
        array:41 [ "USER" => "www-data" "HOME" => "/var/www" "HTTP_ACCEPT_ENCODING" => "gzip, deflate, br, zstd" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_CONNECTION" => "keep-alive" "HTTP_HOST" => "s8.schoolap.com" "REDIRECT_STATUS" => "200" "SERVER_NAME" => "s8.schoolap.com" "SERVER_PORT" => "443" "SERVER_ADDR" => "188.166.147.66" "REMOTE_PORT" => "35353" "REMOTE_ADDR" => "52.15.65.43" "SERVER_SOFTWARE" => "nginx/1.18.0" "GATEWAY_INTERFACE" => "CGI/1.1" "HTTPS" => "on" "REQUEST_SCHEME" => "https" "SERVER_PROTOCOL" => "HTTP/1.1" "DOCUMENT_ROOT" => "/var/www/s8.schoolap.com/public" "DOCUMENT_URI" => "/index.php" "REQUEST_URI" => "/lessons/832/expression-particulier-de-chute-libre" "SCRIPT_NAME" => "/index.php" "CONTENT_LENGTH" => "" "CONTENT_TYPE" => "" "REQUEST_METHOD" => "GET" "QUERY_STRING" => "" "SCRIPT_FILENAME" => "/var/www/s8.schoolap.com/public/index.php" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/index.php" "REQUEST_TIME_FLOAT" => 1746146223.1613 "REQUEST_TIME" => 1746146223 ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Fri, 02 May 2025 00:37:03 GMT" ] "set-cookie" => array:3 [ 0 => "lang_schoolap=eyJpdiI6ImlMY0JPaThQVnE1S1p6UlpGMlRFSFE9PSIsInZhbHVlIjoiQzEra2J2ek9iRnlqU0pGU3VETzZTNXZNS1VLblZ1VGpFN010QWFWNkN2M01jMk9KcU4ybys4L2VxdkRvYkZQQyIsIm1hYyI6ImM5ZjBiOGVjOTg1MTEzNzdhZjA1NmRmN2M4Y2M4NTI2ZmUwZGE4NDZkMGUwZTExOWRkMWQ5MmJhOTY3OTE4NzYiLCJ0YWciOiIifQ%3D%3D; expires=Thu, 08 May 2025 23:17:03 GMT; Max-Age=600000; path=/; httponly; samesite=laxlang_schoolap=eyJpdiI6ImlMY0JPaThQVnE1S1p6UlpGMlRFSFE9PSIsInZhbHVlIjoiQzEra2J2ek9iRnlqU0pGU3VETzZTNXZNS1VLblZ1VGpFN010QWFWNkN2M01jMk9KcU4ybys4L2VxdkRvYkZQQyIsIm" 1 => "XSRF-TOKEN=eyJpdiI6InBzTlozS0h5eXFLeWtUZXhuSnNRanc9PSIsInZhbHVlIjoic3Fid0s1TEhHdGljcCtENmJmR3c0UGVyZ0UrL3dublhFTnFaMDR4bFJrNWJmcmFXRUt1NnVwRngrQk1QQlZ4N3B1UXZKSjRCeGNGQWZXOGJzNnBTVmxVNlZpaWxNa2luT0wxdDFRam55YW5xT0p2RHlseC9KdXZmS3VrUFR6dmoiLCJtYWMiOiIzNmI5OGFmYmRhMzQzNjBmZjgwZTlmYzQ0MDA5M2JiMTFiZmFhNGU0NjRlYTkyNGYxMDlhYTBiYzZjMzgyNjNhIiwidGFnIjoiIn0%3D; expires=Fri, 02 May 2025 02:37:03 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6InBzTlozS0h5eXFLeWtUZXhuSnNRanc9PSIsInZhbHVlIjoic3Fid0s1TEhHdGljcCtENmJmR3c0UGVyZ0UrL3dublhFTnFaMDR4bFJrNWJmcmFXRUt1NnVwRngrQk1QQlZ4N3B1UXZKS" 2 => "schoolap_session=eyJpdiI6IjlrZnlSVGNrOE5OUEZ2OWdyNzE5MHc9PSIsInZhbHVlIjoiQjNUaGVIUEF4Q0l1YkE3cmViOHEvVE9ld0VxWWdONnNoeXA2NnhwbTQxY0xPUHRBbkJQSENLemc1ZEtuVXVNb2wwdkVENStOWVdiUm1mVGIwNGlJdnhOYjBrZDk2QmFNdlVsdEk2ZGhNSjJ3TmhHR2l1NzFmTk1rcnowdFo3d3giLCJtYWMiOiI3ZTRmNmFkMzQ5Y2M4MmFhMTgxNWM4NjBhYTEzOGRjYzY0OTg3ZjkxMTkwOGVkNDVkZDlhMjczNWM2OWM3OTRjIiwidGFnIjoiIn0%3D; expires=Fri, 02 May 2025 02:37:03 GMT; Max-Age=7200; path=/; httponly; samesite=laxschoolap_session=eyJpdiI6IjlrZnlSVGNrOE5OUEZ2OWdyNzE5MHc9PSIsInZhbHVlIjoiQjNUaGVIUEF4Q0l1YkE3cmViOHEvVE9ld0VxWWdONnNoeXA2NnhwbTQxY0xPUHRBbkJQSENLemc1ZEtuVXVNb2w" ] "Set-Cookie" => array:3 [ 0 => "lang_schoolap=eyJpdiI6ImlMY0JPaThQVnE1S1p6UlpGMlRFSFE9PSIsInZhbHVlIjoiQzEra2J2ek9iRnlqU0pGU3VETzZTNXZNS1VLblZ1VGpFN010QWFWNkN2M01jMk9KcU4ybys4L2VxdkRvYkZQQyIsIm1hYyI6ImM5ZjBiOGVjOTg1MTEzNzdhZjA1NmRmN2M4Y2M4NTI2ZmUwZGE4NDZkMGUwZTExOWRkMWQ5MmJhOTY3OTE4NzYiLCJ0YWciOiIifQ%3D%3D; expires=Thu, 08-May-2025 23:17:03 GMT; path=/; httponlylang_schoolap=eyJpdiI6ImlMY0JPaThQVnE1S1p6UlpGMlRFSFE9PSIsInZhbHVlIjoiQzEra2J2ek9iRnlqU0pGU3VETzZTNXZNS1VLblZ1VGpFN010QWFWNkN2M01jMk9KcU4ybys4L2VxdkRvYkZQQyIsIm" 1 => "XSRF-TOKEN=eyJpdiI6InBzTlozS0h5eXFLeWtUZXhuSnNRanc9PSIsInZhbHVlIjoic3Fid0s1TEhHdGljcCtENmJmR3c0UGVyZ0UrL3dublhFTnFaMDR4bFJrNWJmcmFXRUt1NnVwRngrQk1QQlZ4N3B1UXZKSjRCeGNGQWZXOGJzNnBTVmxVNlZpaWxNa2luT0wxdDFRam55YW5xT0p2RHlseC9KdXZmS3VrUFR6dmoiLCJtYWMiOiIzNmI5OGFmYmRhMzQzNjBmZjgwZTlmYzQ0MDA5M2JiMTFiZmFhNGU0NjRlYTkyNGYxMDlhYTBiYzZjMzgyNjNhIiwidGFnIjoiIn0%3D; expires=Fri, 02-May-2025 02:37:03 GMT; path=/XSRF-TOKEN=eyJpdiI6InBzTlozS0h5eXFLeWtUZXhuSnNRanc9PSIsInZhbHVlIjoic3Fid0s1TEhHdGljcCtENmJmR3c0UGVyZ0UrL3dublhFTnFaMDR4bFJrNWJmcmFXRUt1NnVwRngrQk1QQlZ4N3B1UXZKS" 2 => "schoolap_session=eyJpdiI6IjlrZnlSVGNrOE5OUEZ2OWdyNzE5MHc9PSIsInZhbHVlIjoiQjNUaGVIUEF4Q0l1YkE3cmViOHEvVE9ld0VxWWdONnNoeXA2NnhwbTQxY0xPUHRBbkJQSENLemc1ZEtuVXVNb2wwdkVENStOWVdiUm1mVGIwNGlJdnhOYjBrZDk2QmFNdlVsdEk2ZGhNSjJ3TmhHR2l1NzFmTk1rcnowdFo3d3giLCJtYWMiOiI3ZTRmNmFkMzQ5Y2M4MmFhMTgxNWM4NjBhYTEzOGRjYzY0OTg3ZjkxMTkwOGVkNDVkZDlhMjczNWM2OWM3OTRjIiwidGFnIjoiIn0%3D; expires=Fri, 02-May-2025 02:37:03 GMT; path=/; httponlyschoolap_session=eyJpdiI6IjlrZnlSVGNrOE5OUEZ2OWdyNzE5MHc9PSIsInZhbHVlIjoiQjNUaGVIUEF4Q0l1YkE3cmViOHEvVE9ld0VxWWdONnNoeXA2NnhwbTQxY0xPUHRBbkJQSENLemc1ZEtuVXVNb2w" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "C4N11f00JaKmuz1VuPi5PiEJWy6ITw2Ff8JdPuif" "applocale" => "en" "_previous" => array:1 [ "url" => "https://s8.schoolap.com/lessons/832/expression-particulier-de-chute-libre" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]