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Giải mục 2 trang 96 SGK Toán 11 tập 2 - Kết nối tri thức

Xét một chuyển động có phương trình (s = 4cos 2pi t.)

🐈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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HĐ 2

Video hướng dẫn giải

Xét một chuyển động có phương trình \(s = 4\cos 2\pi t.\) a) Tìm vận tốc tức thời của chuyển động tại thời điểm t. b) Tính gia tốc tức thời tại thời điểm t.

Phương pháp giải:

Ý nghĩa vật lí: \(v = s'\) \(a\left( t \right) = v'\left( t \right)\)

Lời giải chi tiết:

a) Ta có \(v = s' =  - 4.2\pi \sin 2\pi t =  - 8\pi \sin 2\pi t\) Vậy vận tốc tức thời của chuyển động tại thời điểm t là \( - 8\pi \sin 2\pi t\) b) \(a\left( t \right) = v'\left( t \right) = {\left( { - 8\pi \sin 2\pi t} \right)^,} =  - 8\pi .2\pi \cos 2\pi t =  - 16{\pi ^2}\cos 2\pi t\)

VD

Video hướng dẫn giải

Một vật chuyển động thẳng có phương trình \(s = 2{t^2} + \frac{1}{2}{t^4}\) (s tính bằng mét, t tính bằng giây). Tìm gia tốc của vật tại thời điểm t = 4 giây.

Phương pháp giải:

Sử dụng công thức \(a = s''\)

Lời giải chi tiết:

Vận tốc tại thời điểm t là \(v\left( t \right) = s' = 4t + 2{t^3}\) Gia tốc tức thời của vật tại thời điểm t là \(a\left( t \right) = v'\left( t \right) = 4 + 6{t^2}\)

Tại thời điểm t = 4 giây, gia tốc của vật là \(a\left( 4 \right) = 4 + {6.4^2} = 100\)(m/s2)

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