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Консультация № 187320
08.05.2013, 22:49
78.80 руб.
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Материальная точка движется прямолинейно, причем так, что её кинетическая энергия в момент t прямо пропорциональна средней скорости движения в интервале от нуля до t . Известно, что при t=0 путь s=0. Показать, что движение равномерно.
Материальная точка движется прямолинейно, причем так, что её кинетическая энергия в момент t прямо пропорциональна средней скорости движения в интервале от нуля до t . Известно, что при t=0 путь s=0. Показать, что движение равномерно.
Обсуждение
09.05.2013, 00:53
общий
это ответ
Здравствуйте, Саша!
В общем-то, по анализу задача.
Мы знаем, что
.
.
Продифференцируем по времени.
.
v = 0 -- конечно решение. Но скучное. Пусть
.
.
Пусть u=v-A.
,
,
.
Т.е. скорость может иметь лишь такой вид:
.
.
Подставим это в исходное уравнение.
.
Откуда B = 0.
Т.е. v постоянно. Что и надо было показать.
В общем-то, по анализу задача.
Мы знаем, что
..Продифференцируем по времени.
.v = 0 -- конечно решение. Но скучное. Пусть
..Пусть u=v-A.
,,.Т.е. скорость может иметь лишь такой вид:
..Подставим это в исходное уравнение.
.Откуда B = 0.
Т.е. v постоянно. Что и надо было показать.
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