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Bài 5 trang 76 SGK Toán 11 tập 2 - Cánh Diều

Vận tốc của một chất điểm chuyển động được biểu thị bởi công thức \(v(t) = 2t + {t^2}\)

൲Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Cánh diều

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Đề bài

Vận tốc của một chất điểm chuyển động được biểu thị bởi công thức \(v(t) = 2t + {t^2}\), trong đó t > 0, t tính bằng giây và v(t) tính bằng m/s. Tìm gia tức thời của chất điểm: a)     Tại thời điểm t = 3(s) b)    Tại thời điểm mà vận tốc của chất điểm bằng 8 m/s

Phương pháp giải - Xem chi tiết

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Lời giải chi tiết

Gia tốc tức thời của chất điểm: \(a(t) = 2t + 2\)a)     Tại thời điểm t = 3(s), gia tốc tức thời của chất điểm là: \(a(3) = 2.3 + 2 = 8\,\left( {m/{s^2}} \right)\)b)    Tại thời điểm mà vận tốc có chất điểm bằng 8 m/s, ta có: \(2t + {t^2} = 8 \Leftrightarrow {t^2} + 2t - 8 = 0 \Leftrightarrow \left[ \begin{array}{l}t = 2 (TMĐK)\,\,\,\,\,\,\\t =  - \,4 (Loại)\,\,\,\,\end{array} \right.\)Với \(t = 2 \Rightarrow a(2) = 2.2 + 2 = 6\)

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

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