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Giải bài 4.20 trang 13 sách bài tập toán 12 - Kết nối tri thức

Vận tốc (v) của một vật rơi tự do từ trạng thái đứng yên được cho bởi công thức (vleft( t right) = 9,8t), trong đó vận tốc (v) tính bằng m/s và thời gian t tính bằng giây. a) Biểu thị quãng đường vật đi được trong T giây đầu tiên dưới dạng tích phân. b) Tìm quãng đường vật đi được trong 5 giây đầu tiên.

🧸Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

Vận tốc \(v\) của một vật rơi tự do từ trạng thái đứng yên được cho bởi công thức \(v\left( t \right) = 9,8t\), trong đó vận tốc \(v\) tính bằng m/s và thời gian t tính bằng giây. a) Biểu thị quãng đường vật đi được trong T giây đầu tiên dưới dạng tích phân. b) Tìm quãng đường vật đi được trong 5 giây đầu tiên.      

Phương pháp giải - Xem chi tiết

Ý a: Tính \(\int\limits_0^T {v\left( t \right)dt} \), kết quả là một biểu thức chứa T. Ý b: Tính \(\int\limits_0^5 {v\left( t \right)dt} \), sử dụng kết quả từ ý a.

Lời giải chi tiết

a) Quãng đường vật đi được trong T giây đầu tiên là \(\int\limits_0^T {v\left( t \right)dt}  = \int\limits_0^T {9,8tdt}  = 9,8 \cdot \left. {\frac{{{t^2}}}{2}} \right|_0^T = 4,9{T^2}\) (m). b) Quãng đường vật đi được trong 5 giây đầu tiên là \(\int\limits_0^5 {v\left( t \right)dt}  = 4,9 \cdot {5^2} = 122,5\)(m).

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