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Консультация № 199320
15.10.2020, 20:07
0.00 руб.
1
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1
Здравствуйте! У меня возникли сложности с таким вопросом: Материальная точка движется вдоль оси Ox так, что график зависимости проекции ее скорости на эту ось от времени имеет вид приведенный на рисунке. Определите модуль средней скорости перемещения этой точки за первые пять секунд движения.
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Обсуждение
16.10.2020, 22:37
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это ответ
Здравствуйте, Ника!
Площадь фигуры под графиком скорости численно равна перемещению на данном отрезке времени. При этом площади фигур над осью времени положительны, а под осью времени отрицательны. То есть, площадь двух верхних треугольников на вашем графике численно равна перемещению вдоль оси х в её положительном направлении, а площадь нижнего треугольника равна перемещению в отрицательном направлении оси х.
Я их подкрасил немножко. Видно, что площадь "положительного" красного треугольника равна по модулю площади зеленого "отрицательного", следовательно в сумме перемещение за последние 4 с движения равно нулю. Остается посчитать перемещение за первую секунду.
Рассчитаем площадь белого неподкрашенного треугольника. А заодно и перемещение за первую секунду.
S1=v*t1/2=1м/с*1с/2=0,5 м
Тогда перемещение за 5 с
S=S1+(Sзел+Sкрас)=S1+0=0,5 м
Тогда средняя скорость перемещения
<v>=S/t=0,5м/5с=0,1 м/с
Площадь фигуры под графиком скорости численно равна перемещению на данном отрезке времени. При этом площади фигур над осью времени положительны, а под осью времени отрицательны. То есть, площадь двух верхних треугольников на вашем графике численно равна перемещению вдоль оси х в её положительном направлении, а площадь нижнего треугольника равна перемещению в отрицательном направлении оси х.
Я их подкрасил немножко. Видно, что площадь "положительного" красного треугольника равна по модулю площади зеленого "отрицательного", следовательно в сумме перемещение за последние 4 с движения равно нулю. Остается посчитать перемещение за первую секунду.
Рассчитаем площадь белого неподкрашенного треугольника. А заодно и перемещение за первую секунду.
S1=v*t1/2=1м/с*1с/2=0,5 м
Тогда перемещение за 5 с
S=S1+(Sзел+Sкрас)=S1+0=0,5 м
Тогда средняя скорость перемещения
<v>=S/t=0,5м/5с=0,1 м/с
5
Спасибо большое!
Об авторе:
С уважением
shvetski
С уважением
shvetski
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