Đáp án:
1. \( - \dfrac{{5\sqrt 3 }}{2}cm\)
2. \( - 61,88cm/s\)
Giải thích các bước giải:
1. Khi \(v = 10\pi \sqrt 3 cm/s\):
\(\begin{array}{l}
\sin \alpha = \dfrac{{10\pi \sqrt 3 }}{{5.4\pi }} = \dfrac{{\sqrt 3 }}{2} \Rightarrow \alpha = \dfrac{\pi }{3}\\
\Rightarrow \varphi = - \dfrac{2}{3}\pi
\end{array}\)
Sau \(t = \dfrac{3}{8}s \Rightarrow \beta = \dfrac{3}{2}\pi \)
\( \Rightarrow \varphi ' = \dfrac{{5\pi }}{6} \Rightarrow x = 5\cos \dfrac{{5\pi }}{6} = - \dfrac{{5\sqrt 3 }}{2}cm\)
2. Khi \(a = 4m/{s^2} = 400cm/{s^2}\):
\(\cos \alpha = \dfrac{{400}}{{5.16.10}} = \dfrac{1}{2} \Rightarrow \alpha = \dfrac{\pi }{3}\)
\( \Rightarrow \varphi = \dfrac{{2\pi }}{3}\)
Sau \(t = \dfrac{4}{9}s \Rightarrow \beta = \dfrac{{16}}{9}\pi \):
\( \Rightarrow \varphi ' = \dfrac{{4\pi }}{9} \Rightarrow v = - 20\pi \sin \dfrac{{4\pi }}{9} = - 61,88cm/s\)
