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Física/1. Tópicos Fundamentais/Exercícios/Cinemática/Movimento uniforme e uniformemente variado.md
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@ -3,15 +3,15 @@ Que distância seu carro percorre a $88km/h$ durante $1s$ em que você olha um a
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### 📄 Solução 1 ### 📄 Solução 1
$\LARGE v=88km/h$ $v=88km/h$
$\LARGE t=1s$ $t=1s$
$\LARGE \Delta S = v \cdot \Delta t \Rightarrow$ $\Delta S = v \cdot \Delta t \Rightarrow$
$\LARGE S_f - S_0 = v \cdot (t_f - t_0)$ $S_f - S_0 = v \cdot (t_f - t_0)$
$\LARGE S_f - S_0 = 88km/h \cdot 1s$ $S_f - S_0 = 88km/h \cdot 1s$
$\LARGE S_f - S_0 = \dfrac{88}{3,6} m*s^{-1} \cdot 1s$ $S_f - S_0 = \dfrac{88}{3,6} m*s^{-1} \cdot 1s$
$\LARGE S_f - S_0 = \dfrac{88}{3,6} m$ $S_f - S_0 = \dfrac{88}{3,6} m$
$\LARGE \Delta S = \dfrac{88}{3,6} m = 24,4\cdots m$ $\Delta S = \dfrac{88}{3,6} m = 24,4\cdots m$
🧐 **Resposta:** $24,4m$ 🧐 **Resposta:** $24,4m$
@ -25,85 +25,85 @@ Que distância seu carro percorre a $88km/h$ durante $1s$ em que você olha um a
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### 📄 Solução 7.1: ### 📄 Solução 7.1:
$\LARGE v_1 = 56,3km/h$ $v_1 = 56,3km/h$
$\LARGE v_2 = 88,5km/h$ $v_2 = 88,5km/h$
$\LARGE v_m = \dfrac{v_1 + v_2}{2}$ $v_m = \dfrac{v_1 + v_2}{2}$
$\LARGE v_m = \dfrac{56,3km/h + 88,5km/h}{2}$ $v_m = \dfrac{56,3km/h + 88,5km/h}{2}$
$\LARGE v_m = \dfrac{144,8km/h}{2} = 72,4km/h$ $v_m = \dfrac{144,8km/h}{2} = 72,4km/h$
--- ---
### 📄 Solução 7.2 ### 📄 Solução 7.2
$\LARGE v_1 = 56,3km/h = \dfrac{\Delta S}{t_1 \cdot 2}$ $v_1 = 56,3km/h = \dfrac{\Delta S}{t_1 \cdot 2}$
$\LARGE v_2 = 88,5km/h = \dfrac{\Delta S}{t_2 \cdot 2}$ $v_2 = 88,5km/h = \dfrac{\Delta S}{t_2 \cdot 2}$
$\LARGE v_m = \dfrac{\Delta S}{\Delta t}$ $v_m = \dfrac{\Delta S}{\Delta t}$
$\LARGE t_1 = \dfrac{\Delta S}{v_1 \cdot 2}$ $t_1 = \dfrac{\Delta S}{v_1 \cdot 2}$
$\LARGE t_2 = \dfrac{\Delta S}{v_2 \cdot 2}$ $t_2 = \dfrac{\Delta S}{v_2 \cdot 2}$
$\LARGE v_m = \dfrac{\Delta S}{\dfrac{\Delta S}{v_1 \cdot 2} + \dfrac{\Delta S}{v_2 \cdot 2}}$ $v_m = \dfrac{\Delta S}{\dfrac{\Delta S}{v_1 \cdot 2} + \dfrac{\Delta S}{v_2 \cdot 2}}$
$\LARGE v_m = \dfrac{\Delta S}{\Delta S \cdot (\dfrac{1}{v_1 \cdot 2} + \dfrac{1}{v_2 \cdot 2})}$ $v_m = \dfrac{\Delta S}{\Delta S \cdot (\dfrac{1}{v_1 \cdot 2} + \dfrac{1}{v_2 \cdot 2})}$
$\LARGE v_m = \dfrac{1}{(\dfrac{1}{v_1 \cdot 2} + \dfrac{1}{v_2 \cdot 2})}$ $v_m = \dfrac{1}{(\dfrac{1}{v_1 \cdot 2} + \dfrac{1}{v_2 \cdot 2})}$
$\LARGE v_m = \dfrac{1}{\dfrac{1}{56,3km/h \cdot 2} + \dfrac{1}{88,5km/h \cdot 2}}$ $v_m = \dfrac{1}{\dfrac{1}{56,3km/h \cdot 2} + \dfrac{1}{88,5km/h \cdot 2}}$
$\LARGE v_m = \dfrac{1}{\dfrac{1}{112,6km/h} + \dfrac{1}{177km/h}}$ $v_m = \dfrac{1}{\dfrac{1}{112,6km/h} + \dfrac{1}{177km/h}}$
$\LARGE v_m = \dfrac{1}{\dfrac{1}{112,6km/h} + \dfrac{1}{177km/h}}$ $v_m = \dfrac{1}{\dfrac{1}{112,6km/h} + \dfrac{1}{177km/h}}$
$\LARGE \dfrac{1}{v_m} = {\dfrac{1}{112,6km/h} + \dfrac{1}{177km/h}}$ $\dfrac{1}{v_m} = {\dfrac{1}{112,6km/h} + \dfrac{1}{177km/h}}$
$\LARGE \dfrac{1}{v_m} = {\dfrac{177km/h}{112,6km/h \cdot 177km/h} + \dfrac{112,6km/h}{112,6km/h \cdot 177km/h}}$ $\dfrac{1}{v_m} = {\dfrac{177km/h}{112,6km/h \cdot 177km/h} + \dfrac{112,6km/h}{112,6km/h \cdot 177km/h}}$
$\LARGE \dfrac{1}{v_m} = {\dfrac{177km/h + 112,6km/h}{112,6km/h \cdot 177km/h}}$ $\dfrac{1}{v_m} = {\dfrac{177km/h + 112,6km/h}{112,6km/h \cdot 177km/h}}$
$\LARGE \dfrac{1}{v_m} = {\dfrac{289,6km * h^{-1}}{19930,2km^2 h^{-2}}}$ $\dfrac{1}{v_m} = {\dfrac{289,6km * h^{-1}}{19930,2km^2 h^{-2}}}$
$\LARGE v_m = \dfrac{19930,2km^2 h^{-2}}{289,6km * h^{-1}}$ $v_m = \dfrac{19930,2km^2 h^{-2}}{289,6km * h^{-1}}$
$\LARGE v_m = \dfrac{19930,2km/h}{289,6}$ $v_m = \dfrac{19930,2km/h}{289,6}$
$\LARGE v_m = 68,819751381 km/h$ $v_m = 68,819751381 km/h$
--- ---
### 📄 Solução 7.3 ### 📄 Solução 7.3
$\LARGE v_{m_{ida}} = 72,4 km/h$ $v_{m_{ida}} = 72,4 km/h$
$\LARGE v_{m_{volta}} = 68,82 km/h$ $v_{m_{volta}} = 68,82 km/h$
$\LARGE v_m = \dfrac{v_{m_{ida}} * t_{ida} + v_{m_{volta}} * t_{volta}}{t_{ida} + t_{volta}}$ $v_m = \dfrac{v_{m_{ida}} * t_{ida} + v_{m_{volta}} * t_{volta}}{t_{ida} + t_{volta}}$
$\LARGE v_m = \dfrac{2d}{t_{ida} + t_{volta}}$ $v_m = \dfrac{2d}{t_{ida} + t_{volta}}$
$\LARGE v_{ida} = \dfrac{d}{t_{ida}} \Rightarrow t_{ida} = \dfrac{d}{v_{ida}}$ $v_{ida} = \dfrac{d}{t_{ida}} \Rightarrow t_{ida} = \dfrac{d}{v_{ida}}$
$\LARGE v_{volta} = \dfrac{d}{t_{volta}} \Rightarrow t_{volta} = \dfrac{d}{v_{volta}}$ $v_{volta} = \dfrac{d}{t_{volta}} \Rightarrow t_{volta} = \dfrac{d}{v_{volta}}$
$\LARGE v_m = \dfrac{2d}{\dfrac{d}{v_{ida}} + \dfrac{d}{v_{volta}}}$ $v_m = \dfrac{2d}{\dfrac{d}{v_{ida}} + \dfrac{d}{v_{volta}}}$
$\LARGE v_m = \dfrac{2}{\dfrac{1}{v_{ida}} + \dfrac{1}{v_{volta}}}$ $v_m = \dfrac{2}{\dfrac{1}{v_{ida}} + \dfrac{1}{v_{volta}}}$
$\LARGE v_m = \dfrac{2}{\dfrac{1}{72,4} + \dfrac{1}{68,82}}$ $v_m = \dfrac{2}{\dfrac{1}{72,4} + \dfrac{1}{68,82}}$
$\LARGE \dfrac{1}{v_m} = \dfrac{\dfrac{1}{72,4} + \dfrac{1}{68,82}}{2}$ $\dfrac{1}{v_m} = \dfrac{\dfrac{1}{72,4} + \dfrac{1}{68,82}}{2}$
$\LARGE \dfrac{2}{v_m} = \dfrac{1}{72,4} + \dfrac{1}{68,82}$ $\dfrac{2}{v_m} = \dfrac{1}{72,4} + \dfrac{1}{68,82}$
$\LARGE \dfrac{2}{v_m} = \dfrac{68,82}{68,82 * 72,4} + \dfrac{72,4}{68,82 * 72,4}$ $\dfrac{2}{v_m} = \dfrac{68,82}{68,82 * 72,4} + \dfrac{72,4}{68,82 * 72,4}$
$\LARGE \dfrac{2}{v_m} = \dfrac{68,82}{4982,568} + \dfrac{72,4}{4982,568}$ $\dfrac{2}{v_m} = \dfrac{68,82}{4982,568} + \dfrac{72,4}{4982,568}$
$\LARGE \dfrac{2}{v_m} = \dfrac{141,22}{4982,568}$ $\dfrac{2}{v_m} = \dfrac{141,22}{4982,568}$
$\LARGE \dfrac{v_m}{2} = \dfrac{4982,568}{141,22} = 35,282311287$ $\dfrac{v_m}{2} = \dfrac{4982,568}{141,22} = 35,282311287$
$\LARGE v_m = 35,282311287 * 2 = 70,56 km/h$ $v_m = 35,282311287 * 2 = 70,56 km/h$
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## 📌 Questão 9 ## 📌 Questão 9