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vault backup: 2025-01-05 11:39:17

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Álvaro Antônio de Lacerda Rosário 2025-01-05 11:39:17 -03:00
parent 1bc4a782de
commit 1e3816f38f
2 changed files with 22 additions and 15 deletions
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6
.obsidian/workspace.json vendored
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@ -77,7 +77,8 @@
}
],
"direction": "horizontal",
"width": 300
"width": 300,
"collapsed": true
},
"right": {
"id": "2088ebc677233f02",
@ -160,7 +161,8 @@
}
],
"direction": "horizontal",
"width": 300
"width": 300,
"collapsed": true
},
"left-ribbon": {
"hiddenItems": {

31
Física/1. Tópicos Fundamentais/Exercícios/Cinemática/Movimento uniforme.md
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@ -264,19 +264,24 @@ $$
\dfrac{x(2) + x(3)}{2} = \dfrac{21,75 + 50,25}{2} = 36 \\
$$
$$
36 = 9,75 + 1,50 t^3 \Rightarrow \\
1,50t ^3 = 36 - 9,75 \Rightarrow \\
1,50t ^3 = 26,25 \Rightarrow \\
t^3 = 17,5 \Rightarrow \\
t = \sqrt[3]{17,5} \\
\\
f'(t) = 4,5 t ^2 \Rightarrow \\
f'(\sqrt[3]{17,5}) = 4,5 \cdot (\sqrt[3]{17,5}) ^2 = 4,5 \cdot \sqrt[3]{17,5^2} \Rightarrow \\
f'(\sqrt[3]{17,5}) = 4,5 \cdot \sqrt[3]{17,5^3 \cdot 17,5^{-1}} \Rightarrow \\
f'(\sqrt[3]{17,5}) = 4,5 \cdot 17,5^{-1} \Rightarrow \\
f'(\sqrt[3]{17,5}) = 4,5 \cdot \dfrac{1}{17,5} = \dfrac{4,5}{17,5} \Rightarrow \\
f'(\sqrt[3]{17,5}) = 4,5 \cdot \dfrac{1}{17,5} = \dfrac{4,5}{17,5} \Rightarrow \\
\begin{align*}
36 &= 9,75 + 1,50 t^3 \Rightarrow \\
1,50t ^3 &= 36 - 9,75 \Rightarrow \\
1,50t ^3 &= 26,25 \Rightarrow \\
t^3 &= 17,5 \Rightarrow \\
t &= \sqrt[3]{17,5} \\
\end{align*}
$$
$$
\begin{align*}
f'(t) &= 4,5 t ^2 \\
&= 4,5 \cdot (\sqrt[3]{17,5}) ^2 \\
&= 4,5 \cdot \sqrt[3]{17,5^2} \\
&= 4,5 \cdot \sqrt[3]{17,5^3 \cdot 17,5^{-1}} \\
&= 4,5 \cdot 17,5^{-1} \\
&= 4,5 \cdot \dfrac{1}{17,5} = \dfrac{4,5}{17,5} \\
&= 4,5 \cdot \dfrac{1}{17,5} = \dfrac{4,5}{17,5} \\
\end{align*}
$$
🧐 **Resposta:** $2,1m/s$