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Здравствуйте! У меня возникли сложности с таким вопросом: Материальная точка движется по окружности диаметром 40 м. Зависимость пути от времени её движения определяется уравнением S= t³+4•t²-t+8. Определить пройденный путь, скорость, тангенциальное, нормальное и полное ускорения движущейся точки через 4 сек после начала движения.
v=(s)'=3t^2+8t-1 а(полн)=(v)'=6t+8 a(цс)=v^2/R а(танг)=корень из (a(полн)^2-а(цс)^2) Необходимо просто подставить t=4? тогда а полн=32 м/c в квадрате, а ц.с 312 м/c в квадрате
Неправильно. Производная скорости -- это тангенциальное ускорение. Мы рассматриваем движение по окружности, то есть по кривой линии постоянной кривизны.
v=(s)'=3t^2+8t-1, тогда v=3*4^2+8*4-1=79 атангенц=(v)'=6t+8 тогда а=6*4+8=32 a(цс)=v^2/R= 79^2/20=312 аполн=корень из (a(танг)^2+а(цс)^2)=корень 32^2+312^2=314
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mari_nikopol 
Гордиенко Андрей Владимирович 
