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Bài 9.12 trang 94 SGK Toán 11 tập 2 - Kết nối tri thức

Chuyển động của một hạt trên một dây rung được cho bởi (sleft( t right) = 12 + 0,5sin left( {4pi t} right),)

💯Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Chuyển động của một hạt trên một dây rung được cho bởi \(s\left( t \right) = 12 + 0,5\sin \left( {4\pi t} \right),\) trong đó s tính bằng centimét và t tính bằng giây. Tính vận tốc của hạt sau t giây. Vận tốc cực đại của hạt là bao nhiêu?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

- Ý nghĩa vật lí: \(v = s'\) - Sử dụng công thức \(\left( {\sin u} \right)' = u'.\cos u\)

Lời giải chi tiết

Ta có \(v\left( t \right) = s'\left( t \right) = 0,5.\left( {4\pi t} \right)'\cos \left( {4\pi t} \right) = 2\pi \cos \left( {4\pi t} \right)\) Vì \( - 1 \le \cos \left( {4\pi t} \right) \le 1 \Leftrightarrow  - 2\pi  \le 2\pi \cos \left( {4\pi t} \right) \le 2\pi  \Leftrightarrow  - 2\pi  \le v\left( t \right) \le 2\pi \) Do đó vận tốc cực đại của hạt là \(2\pi \) cm/s.

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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