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Özellikle hızlanma ve yavaşlama durumlarında hız ve ivmenin yönleri arasındaki ilişki vurgulanmaktadır: hızlanırken hız ve ivme aynı yönlü, yavaşlarken ise zıt yönlü olduğu açıklanmaktadır."]},"endTime":143,"title":"Uğur Böceği ile Hız ve İvme Uygulaması","beginTime":0}],"fullResult":[{"index":0,"title":"Uygulama Tanıtımı","list":{"type":"unordered","items":["Uygulamada Uğur böceğini hareket ettirerek hız ve ivmesinin değişimini görebilirsiniz.","Uygulamada farklı hareket çeşitleri bulunmakta: elle yönlendir (doğrusal), dairesel ve elips şeklinde.","Doğrusal hareket seçildiğinde Uğur böceği sabit hızla hareket eder."]},"beginTime":9,"endTime":47,"href":"/video/preview/4373973678963111038?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=9&ask_summarization=1"},{"index":1,"title":"Hız ve İvme İlişkisi","list":{"type":"unordered","items":["Uğur böceğini elle yönlendirerek hızlandırıldığında, hız ve ivmenin bazı durumlarda 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Öğretmen, öğrencilere hitap ederek konuyu adım adım açıklamaktadır.","Videoda düzgün çembersel harekette etki eden kuvvetler, merkezcil kuvvet ve merkezcil ivme kavramları detaylı şekilde ele alınmaktadır. Öğretmen önce teorik açıklamalar yaparak, bir cismin çembersel hareket yapabilmesi için üzerine etki eden net kuvvetin merkeze doğru olması gerektiğini anlatır, ardından ağırlık kuvveti ve normal kuvvet arasındaki ilişkiyi açıklar. Son olarak, hız değişim vektörünün hesaplanması ve üçgenlerin benzerliği kullanılarak merkezcil ivmenin formülünün (a = v²/r ve a = ω²r) türetilmesi gösterilmektedir.","Video, günlük hayattan örnekler (ip gerilmesi, Dünya-Ay sistemi) kullanarak konuyu pekiştirmekte ve bir deney üzerinden merkezcil kuvvet görevini gören farklı kuvvetleri tanıtmayı planlamaktadır. Ayrıca, hız değişim vektörünün vektörel toplama ile nasıl elde edildiği ve merkezcil ivmenin vektörel gösterimi de açıklanmaktadır."]},"endTime":1478,"title":"Düzgün Çembersel Hareket ve Merkezcil Kuvvet Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Çembersel Hareketin Şartları","list":{"type":"unordered","items":["Bu derste bir cismin çembersel bir yörünge izlemesi için gerekli şartlar ve merkezcil ivme, merkezcil kuvvet kavramları ele alınacaktır.","Bir cismin çembersel hareket yapması için sürekli olarak merkeze doğru bir kuvvet etki etmesi gerekir.","Eğer bir cismin üzerine hiçbir kuvvet etki etmiyorsa, Newton'un eylemsizlik yasasına göre o cisim sürekli aynı hızla doğrusal bir yörünge izler."]},"beginTime":4,"endTime":103,"href":"/video/preview/4293665590132272529?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=4&ask_summarization=1"},{"index":1,"title":"Merkezcil Kuvvet Kavramı","list":{"type":"unordered","items":["Bir cismin sürekli olarak merkeze doğru kuvvetler etki etmesi sonucunda çembersel bir yörünge izlemesine neden olur.","Bu kuvvetlerin ortak noktası çemberin merkez noktasıdır ve bu kuvvetler merkezi gösterdiği için \"merkezcil kuvvet\" olarak adlandırılır.","Bir cisim çembersel hareket yapıyorsa, kesinlikle üzerine bir net kuvvet etki etmektedir ve bu net kuvvet merkeze doğrudur."]},"beginTime":103,"endTime":240,"href":"/video/preview/4293665590132272529?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=103&ask_summarization=1"},{"index":2,"title":"Merkezcil Kuvvet Örnekleri","list":{"type":"unordered","items":["İp ucuna bağlanan bir taş, ip gerilmesi kuvveti sayesinde çembersel hareket yapar ve burada merkezcil kuvvet görevini T (ip gerilmesi) görür.","Dünya-Ay ikilisinde, Ay Dünya'nın etrafında çembersel hareket yaparken, Dünya'nın Ay'a uyguladığı kütle çekim kuvveti merkezcil kuvvet görevini görür.","Merkezcil kuvvet kendi başına yeni bir kuvvet değildir, zaten halihazırda olan bir kuvvetin merkezcil kuvvet görevini görmesi durumudur."]},"beginTime":240,"endTime":515,"href":"/video/preview/4293665590132272529?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=240&ask_summarization=1"},{"index":3,"title":"Çember Çizme ve Kuvvetler","list":{"type":"unordered","items":["Masaya tepeden bakıldığında, cismin üzerine ağırlık kuvveti (G) etki eder ve bu kuvvet ekrandan içeriye doğru gösterilir.","Tepsinin tabanından gelen normal kuvvet (N), ağırlık kuvvetinin tersine doğru (ekrandan dışarıya) etki eder ve bu iki kuvvet birbirini götürür.","Çember çizmek için merkezcil kuvvet gerekir; bu örnekte merkezcil kuvvet görevini yan duvarlardan gelen normal kuvvetler 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İvme","list":{"type":"unordered","items":["Çembersel harekette oluşan ivmenin ismi merkezcil ivmedir ve her zaman merkezi gösterir.","Hız vektörü ile merkezcil kuvvet arasında 90 derecelik açı olduğundan, kuvvet hızı arttırmaz veya azaltmaz, sadece yönünü değiştirir.","Merkezcil ivme (a) birim zamandaki hız değişimidir ve vektörel büyüklüktür."]},"beginTime":875,"endTime":1034,"href":"/video/preview/4293665590132272529?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=875&ask_summarization=1"},{"index":6,"title":"Merkezcil İvme Formüllerinin İspatı","list":{"type":"unordered","items":["Çembersel hareket yapan bir cismin konum vektörü (r) yarıçap vektörü olarak da adlandırılır.","Yer değiştirme vektörü (Δr) ilk konum vektörü (rA) ile son konum vektörü (rB) arasındaki farktır.","Hız değişimini hesaplamak için ilk hız vektörü ile son hız vektörü arasındaki fark bulunur, bu da ivme hesaplamasında kullanılır."]},"beginTime":1034,"endTime":1150,"href":"/video/preview/4293665590132272529?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=1034&ask_summarization=1"},{"index":7,"title":"Hız Değişim Vektörü ve Üçgenler","list":{"type":"unordered","items":["İlk hız vektörü ve son hız vektörü arasındaki fark delta v (Δv) olarak gösterilir.","Hız değişim vektörü, başlangıç ve bitiş hız vektörlerini birleştiren yeşil çizilen vektördür.","Oluşturulan üçgenler, ivme hesaplamalarında geometri kullanmak için önemlidir."]},"beginTime":1152,"endTime":1213,"href":"/video/preview/4293665590132272529?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=1152&ask_summarization=1"},{"index":8,"title":"Benzerlik ve İvme Hesaplama","list":{"type":"unordered","items":["Düzgün çembersel harekette hız büyüklüğü değişmez, bu nedenle başlangıç ve bitiş hız vektörleri eşittir.","İki üçgen benzerdir çünkü her ikisinin de yarıçap uzunluğu eşittir ve aralarındaki açı teta'dır.","Benzerlik ilişkisi kullanılarak Δr/r = Δv/v bağıntısı elde edilir."]},"beginTime":1213,"endTime":1306,"href":"/video/preview/4293665590132272529?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=1213&ask_summarization=1"},{"index":9,"title":"Merkezcil İvme Formülü","list":{"type":"unordered","items":["Hız, birim zamandaki konum değişimidir (Δr/Δt) ve bu bağıntı Δr yerine vΔt olarak yazılabilir.","İvme formülü a = Δv/Δt = v²/r olarak elde edilir.","Merkezcil ivme formülü a = ω²r olarak açısal hız cinsinden de yazılabilir."]},"beginTime":1306,"endTime":1406,"href":"/video/preview/4293665590132272529?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=1306&ask_summarization=1"},{"index":10,"title":"Vektörel Gösterim","list":{"type":"unordered","items":["Merkezcil ivme 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gün en yeni eğitim videolarını ilk izleyen olmak için kanalımıza abone olun. Daha fazlası ve ders videolarını sıralı izlemek için: https://www.khanacademy.org.tr Matematikten sanat tarihine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/2037999/ed67eb5fbd13a44cec204c41013bf247/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/XXKNJgIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"18","reqid":"1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=videoid:15808618215366618704","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik eğitim içeriğidir. Bir eğitmen, Jale adlı bir kişinin tempolu koşu yaptığı bir problemi çözmektedir.","Videoda, Jale'nin hız fonksiyonu (v) kullanılarak v'(16) değerinin nasıl tahmin edileceği anlatılmaktadır. Eğitmen önce problemi açıklayıp, verilen verileri kullanarak v'(16) değerini hesaplama yöntemini göstermekte, ardından bu işlemi görsel olarak bir grafik üzerinde açıklamaktadır. Video, türev kavramını günlük hayattan bir örnek üzerinden anlatarak, verilen verilerle türev değerinin nasıl tahmin edilebileceğini adım adım göstermektedir."]},"endTime":355,"title":"Matematik Dersinde Türev Hesaplama Sorusu Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Jale'nin Hız Fonksiyonu","list":{"type":"unordered","items":["Jale düz bir güzergahta tempolu koşu yapmakta ve 0, ≤ t ≤ 40 dakika aralığında hızı türevlenebilir bir v fonksiyonuyla verilmektedir.","Tabloda t dakika türünden ve v metre/dakika türünden ölçülmüş değerler bulunmaktadır.","Soruda v(16) değeri verilmemiş, ancak v'(16) değerini tahmin etmek istenmektedir."]},"beginTime":0,"endTime":43,"href":"/video/preview/15808618215366618704?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=0&ask_summarization=1"},{"index":1,"title":"Türevin Tahmini","list":{"type":"unordered","items":["v'(16) değeri, t=16 olduğunda v'nin zamana göre değişim oranıdır.","Tahmin etmek için t=12 ile t=20 arasındaki değişim oranını bulmak gerekir.","Hızdaki değişim (v(20) - v(12)) = 240 m, zamandaki değişim (20 - 12) = 8 dakika olduğundan, türev değeri 240/8 = 30 m/dakika² olarak hesaplanır."]},"beginTime":43,"endTime":135,"href":"/video/preview/15808618215366618704?parent-reqid=1769470040403401-13701936095465242579-balancer-l7leveler-kubr-yp-sas-58-BAL&text=Computing4Schools&t=43&ask_summarization=1"},{"index":2,"title":"Grafiksel Gösterim","list":{"type":"unordered","items":["Soruyu görsel olarak anlamak için v(t) fonksiyonunun grafiği çizilebilir.","Grafiğin yatay ekseninde zaman (t), dikey ekseninde hız (v) değerleri yer alır.","Verilen değerler: (0,0), (12,200), (20,240), (24,-220), (40,150) olarak grafikte 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