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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Точка движется в плоскости XOY по закону: x = t/2; y = t(1 – t). Найти уравнение траектории y = f(x) и изобразить ее графически; вектор скорости v и ускорения a в зависимости от времени; модуль скорости в момент времени t = 0,8 с
Вы можете вывести уравнение траектории, если из уравнения x=t/2 выразите t через x и подставите в уравнение y=t(1-t). Тогда получите зависимость y=y(x).
Вы можете вывести уравнение траектории, если из уравнения x=t/2 выразите t через x и подставите в уравнение y=t(1-t). Тогда получите зависимость y=y(x).
Получится причём траекторией является часть параболы, расположенная правее точки
Дифференцируя один раз выражения для и по переменной Вы получите выражения для компонент скорости и причём вектор скорости в каждой точке траектории направлен по касательной к ней, а его модуль равен
Дифференцируя полученные выражения для компонент скорости, Вы получите выражения для компонент ускорения и причём модуль ускорения равен
Об авторе:
Facta loquuntur.
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Гордиенко Андрей Владимирович 
причём траекторией является часть параболы, расположенная правее точки 
и 
по переменной 
Вы получите выражения для компонент скорости 
и 
причём вектор скорости в каждой точке траектории направлен по касательной к ней, а его модуль равен 
и 
причём модуль ускорения равен 