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Консультация № 200997
28.05.2021, 22:51
0.00 руб.
28.05.2021, 22:57
0
3
2
Здравствуйте! У меня возникли сложности с таким вопросом:
Материальная точка начинает двигаться в момент времени [t][0]= из начала координат со скоростью изменяющейся со временем по закону v=iA+jBt+kCt2, где A=1м/c, B=2м/c2, C=1,5м/c3. На каком расстоянии от начала координат окажется эта точка через t=2c после начала движения?
Материальная точка начинает двигаться в момент времени [t][0]= из начала координат со скоростью изменяющейся со временем по закону v=iA+jBt+kCt2, где A=1м/c, B=2м/c2, C=1,5м/c3. На каком расстоянии от начала координат окажется эта точка через t=2c после начала движения?
Обсуждение
29.05.2021, 00:05
общий
29.05.2021, 18:39
это ответ
Здравствуйте, Олег!
Предлагаю Вам следующее решение задачи.
Дано:
с -- момент начала движения материальной точки из начала координат; 
-- зависимость изменения скорости материальной точки от времени.
Определить:
-- расстояние от начала координат, на котором окажется материальная точка в момент времени 
с.
Поскольку материальная точка начинает двигаться из начала координат, то её начальное положение задаётся нулевым вектором. Определим зависимость радиус-вектора материальной точки от времени:
Определим радиус-вектор точки в момент времени с:
(м);
(м).
Ответ:
м.
Предлагаю Вам следующее решение задачи.
Дано:
с -- момент начала движения материальной точки из начала координат; -- зависимость изменения скорости материальной точки от времени.Определить:
-- расстояние от начала координат, на котором окажется материальная точка в момент времени с.Решение
Поскольку материальная точка начинает двигаться из начала координат, то её начальное положение задаётся нулевым вектором. Определим зависимость радиус-вектора материальной точки от времени:
Определим радиус-вектор точки в момент времени
с: (м); (м).Ответ:
м.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
29.05.2021, 00:41
общий
29.05.2021, 10:11
это ответ
Дано:
v=iA+jBt+kCt2
A=1м/c, B=2м/c2, C=1,5м/c3
r0(0;0;0)=0
t1=2c
Найти: r1
Решение:
Уравнение радиус-вектора связано с уравнением скорости таким образом: скорость - это производная радиус-вектора по времени, а радиус-вектор, соответственно, - это интеграл от скорости.
r(t)=[$8747$](iA+jBt+kCt2)dt
Тогда
r(t)=iAt+j(B/2)t2+k(C/3)t3+r0
- здесь
i, j, k - единичные векторы (орты) в трехмерной декартовой системе координат, соответствующие координатным осям x, y и z, а r0=0 - нулевой вектор, соответствующий положению точки в начале отсчета времени.
Координаты точки в момент времени t1, следовательно:
x1=A*t1 = 1м/с*2с = 2м;
y1=(B/2)*t12 = (2/2)м/с2*(2с)2 = 4м;
z1=(C/3)*t13 = (1,5/3)м/с3*(2с)3 = 4м.
Тогда длина радиус-вектора в момент времени t1:
r1=[$8730$](x12+y12+z12) = [$8730$](22+42+42) = 6 м
*******
Удачи
v=iA+jBt+kCt2
A=1м/c, B=2м/c2, C=1,5м/c3
r0(0;0;0)=0
t1=2c
Найти: r1
Решение:
Уравнение радиус-вектора связано с уравнением скорости таким образом: скорость - это производная радиус-вектора по времени, а радиус-вектор, соответственно, - это интеграл от скорости.
r(t)=[$8747$](iA+jBt+kCt2)dt
Тогда
r(t)=iAt+j(B/2)t2+k(C/3)t3+r0
- здесь
i, j, k - единичные векторы (орты) в трехмерной декартовой системе координат, соответствующие координатным осям x, y и z, а r0=0 - нулевой вектор, соответствующий положению точки в начале отсчета времени.
Координаты точки в момент времени t1, следовательно:
x1=A*t1 = 1м/с*2с = 2м;
y1=(B/2)*t12 = (2/2)м/с2*(2с)2 = 4м;
z1=(C/3)*t13 = (1,5/3)м/с3*(2с)3 = 4м.
Тогда длина радиус-вектора в момент времени t1:
r1=[$8730$](x12+y12+z12) = [$8730$](22+42+42) = 6 м
*******
Удачи
Об авторе:
С уважением
shvetski
С уважением
shvetski
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