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Уважаемые эксперты! Пожалуйста, ответьте на вопрос: 1. Время разгона автомобиля до скорости 100 км/ч составляет 10 секунд. Каково при этом среднее ускорение автомобиля? Какой путь он пройдет во время разгона (если предположить, что при разгоне автомобиль двигался равноускоренно)? Какова его средняя скорость во время разгона?
Здравствуйте, ilyasov_azat_danisovich! Из школьной физики\механики вспоминаем простую формулу зависимости пройденного пути от времени при равно-ускоренном движении: S = a*t2/2 + V0 * t + S0 , где a - ускорение, t - время, V0 и S0 - скорость и расстояние в начальный момент времени t=0 . Текущая скорость равна производной пути от времени : V(t) = V0 + a*t
Примем V0=0 и S0=0 , поскольку они НЕ заданы в Условии задачи. Тогда из ещё более простой формулы V(t) = a * t получаем искомое ускорение : a = V(10) / t = 100 * 1000 / 3600 /10 = 2,778 м/сек2
Во время разгона автомобиль проедет S = a * t2 / 2 = 2,778 * 102 /2 = 138,9 метров. Его средняя скорость во время разгона равна половине конечной скорости , то есть 100/2 = 50 км/час или 50/3,6 = 13,9 м/сек.
Позвольте не согласиться: по определению: средняя скорость вычисляется как путь деленный на время. Можно доказать, что Ваше утверждение верно при равноускоренном движении. В иных случаях - нет.
Об авторе:
Понеже не словес красных бог слушает, но дел наших хощет
Вы писали : "по определению: средняя скорость вычисляется как путь деленный на время" - очень уместное и легко-запоминающееся определение! Я учту его на будущее! Спасибо! В процессе решения я также вспоминал способ вычислить скорость, как интеграл от ускорения. Но подумал, что если студент не может решить такую лёгкую задачу самостоятельно, то лучше сразу согласно условию "предположить, что при разгоне автомобиль двигался равноускоренно" и получить среднюю скорость простейшим способом.
виноват, похоже проделки сенсорного экрана планшета.Читал внимательно. Я не помню, чтобы в каком-либо учебнике физики указывалось, что при равноускоренном движении без начальной скорости средняя скорость во время разгона равна половине конечной скорости и был очень удивлён, когда это оказалось именно так. Возможно старею
Об авторе:
Понеже не словес красных бог слушает, но дел наших хощет
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