3. Нүктенің түзусызықты қозғалысы ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAALCAYAAADLA1tMAAAACXBIWXMAAA7PAAAPFAF/FlHwAAAELUlEQVR4nO2WeVCUdRjHPyzLfSzLJQqBCIIgBDSlBFgaVshhamIso6PNJIxlcdgQTuhIYyMRxkh51D/lEShjngmpkIGMQzrSqFiYxKFcySELC7uwsNuyJHGJTDMO/uF35jfzznN+n+/7e955hSqVSs1TIJxqAo8bOvJ71PWLsTfVG7Kp+9opKPgDG8tWzhV1YbEi6vEKUXOjiMMnz9Jw5y5ekZuJedUTubSZNpUp9mKjMfHn87PxXBA5gvQD3LmYQ+qRMkQmxqxPSMbDbjBfIW0g73Qul36tpMPMnrQtyVj11rIpJQOlvgHCHinB7+7E3lNETd3fzHSYho7QguDFPlwv/YnglaHMcewfFKKuvl5b1NzSFnOjQRKqvm5amtvoVemMIDQ85lGQqw1ZE5+KjaKUqLVZhD2fSfnJPRQLFxEf5ouN2HxEfEtzA71KnbF12qrIOJhHSuYhag4lsyu7gH2JEVqfUt6Jw/xI0qPE7FkfRt6tOCQOCjo6nUnd/yHT1YObL6st4eOMc6Qkx2KvmaG84CC31C44G1VzXO6DsDr/Kz4tlOIokCJyW0ncO/O0iT0dTRSePklT1zBGQiP8QyN50cVqUkJ4PDt/cMCKm9gsCMZE2cjlK1e4rlRQYKWLZEngpOrIWm6jNPbG2USNib8PstwquvpVmOgKMLNzZ56dRpDOJqpNZ7DRSR/6obXxIqmJDTh6BBL39jJqKsqovFnG8dxcoiOjud8qoP3+DVrMFuI0TTNa/e0/6XUIZ2v8ayOaG1nOQhKT8EiSP2dKWLzpyEjj7OXcvXpYe8UHCH703V9k7N6AhebtLAwKwEC8EkmImza04UYeK0LCudz4IDlJ09yaLdkXSH1jrtai0gjXI5uYR3nRUfQWJuEsHrjkc/jh7AmtfUfMS2R7BhHl8zrez3WyITERsYbHzHXrCRvKViO0C4llm54ZR9PjqXhmHSkS38Hmk1yNVxJyUGnOeJDWXmN/WStZuz7jgmaP/QLDtfbebsXQvs7wDqW0XqW15xzIwD8i/t9h/oPI1g25PIfqLh3aqupwn+OHrqyJkt9bCHjBlfwz+ZjMfYtPDMo5VNzAm14Kqtv18ZzlgJ/XbH5pbMTYzYB+mVJzGqmUi3C1HvmNEpadz6HwlgxTPV2WLXcdcgiExthON574NUyAASGLTn3PtfJutpacQSmyJyDYEBcvX3I/30uxXYJWiMnA0MaDJEkQaZvjsLXyJDo2gL72qxw79RuzTOv48UQe+sWXONZ5j0Uf7EbWfI19O7PRNxAhsHEnJtoNgUUPwdYKtu07RfzaNWN6CFe9t51V/3vch2NAyKXvp7N0tENzA748EDpuTuDLEViZC8b1+YVv5Ovw4ZYgvtgRpH3a++3oekvI+mbJKJsRq7ensfohfJ+o/whHJ/cp6/1ECTGV+Aftk4MKPEL2lQAAAABJRU5ErkJggg==) теңдеуімен анықталады (-секундпен, -метрмен). 10-секундтың аяғындағы арақашықты, жылдамдық пен үдеуді, сонымен қатар осы уақытта жүріп өткен жолын анықта және арақашықтықтың графигін сал[4].
Шешуі. 1) Берілген қозғалыстың теңдеуін дифференциалдап, жылдамдықтың мынадай теңдеуін аламыз:
2) Уақыттың қандай мәнінде жылдамдық нольге тең болатынын анықтаймыз. Ол үшін жылдамдықыт белгілейтін теңдеуді нольге теңестіреміз және t уақытқа қатысты есептейміз:
3) Жылдамдықтың теңдеуін дифференциалдау арқылы жанамалық үдеудің теңдеуін аламыз. Қозғалыс түзусызықты болғандықтан, толық үдеу жанамалық үдеу –тең болады:
4) График тұрғызу үшін -ның мәні 0-ден 10 с дейінгі аралықта болатын (м), (м/с) сандық мәндері берілген қосымша кестені құрып аламыз. Ескерте кету керек, үдеудің сандық мәні уақыт ағымымен өзгермейді.
мәні
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0
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2
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4
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6
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8
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10
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0
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-3
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-4
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-3
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0
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5
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5) Осы берілген мәндермен құрылған график суретте көрсетілген (![](data:image/png;base64,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) , ![](data:image/png;base64,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) , ![](data:image/png;base64,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) )
Нәтижесінде: 10-шы секундтың аяғында арақашықтық: ![](data:image/png;base64,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) , 10 с жүрілген жол ОА+АО+ОВ=4+4+5=13м, 10-шы с аяғындағы жылдамдық ![](data:image/png;base64,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)
4. Нүкте радиусы 12 м шеңбер бойымен ![](data:image/png;base64,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) теңдеуімен қозғалады (-секундпен, -метрмен). 4 секундтың аяғында нүктенің бастапқы траекториядан қандай арақашықтықта болатынын, сонымен қатар осы уақыттағы жылдамдықты және үдеуді табыңыз[4].
Шешімі. 1) Нүкте қозғалысының теңдеуіне![](data:image/png;base64,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) мәнін қойып, есеп басындығы арақашықтықты табамыз.
Яғни, 4 с кейін нүкте қозғалыс басталған траекторияға қайта келеді.
2) Берілген қозғалыстың теңдеуін дифференциалдап, жылдамдықтың теңдеуін табамыз.
![](data:image/png;base64,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) кезіндегі нүктенің жылдамдығы
3) Жылдамдықтың теңдеуін дифференциалдап, жанамалық үдеуді табамыз:
![](data:image/png;base64,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) кезіндегі нүктенің жанамалық үдеуі
4) 4 с соңындығы нормаль үдеу:
5) 4 с соңындығы толық үдеуді табамыз:
6) Толық үдеудің векторының бағытын анықтаймыз, яғни ![](data:image/png;base64,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)
![](data:image/png;base64,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)
Достарыңызбен бөлісу: |