솔루션피아

$$\ab{a}$$ $$\begin{aligned} x_5&=x_0+\Delta x_{0\rarr5} \\ &=0+\int_0^5 v\dd t \\ &=\frac{1}{2}(2\ut{s}+4\ut{s})8\ut{m/s}+\frac{1}{2}(4\ut{m/s}+8\ut{m/s})1\ut{s}\\ &=30\ut{m} \end{aligned}$$ $$\ab{b}$$ $$v_5=4\ut{m/s}$$ $$\ab{c}$$ $$\begin{aligned} a_5&=\dt v\\ &=\frac{-8\ut{m/s}}{2\ut{s}}\\ &=-4\ut{m/s^2} \end{aligned}$$ $$\ab{d}$$ $$ \begin{aligned} \bar{v}_{1\rarr5}&=\frac{\Delta x_{1\..

$$\begin{cases} H&=100\ut{m}\\ v_0&=0 \end{cases}$$ $$\ab{a}$$ $$2aS=v^2-v_0^2,$$ $$\begin{aligned} v&=\sqrt{2aS+v_0^2}\\ &=\sqrt{2(-g)(-H)+(0)^2}\\ &=\sqrt{2gH}\\ &=\sqrt{2(9.80665\ut{m/s^2})(100\ut{m})}\\ &=\frac{\sqrt{196133}}{10}\ut{m/s}\\ &\approx44.28690551393267\ut{m/s}\\ &\approx4\times10\ut{m/s}\\ \end{aligned}$$ $$\ab{b}$$ $$S=v_0t+\frac{1}{2}at^2,$$ $$ \begin{aligned} t&=\sqrt{\fr..

풀이자주:(b)문제가 묻는것이 불분명하여 임의로 위치를 구했습니다. $$\begin{cases} x\ut{cm}&=5.00(t\ut{sec})-0.500(t\ut{sec})^3\\ &0\lt x\lt15\ut{cm} \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} v&=\dxt{x}=\dt\(5t-0.5t^3\)\\ &=5-1.5t^2=0 \end{aligned}$$ $$\begin{aligned} t&=\sqrt{\frac{5}{1.5}}\ut{sec}\\ &=\sqrt{\frac{10}{3}}\ut{sec}\\ &\approx1.8257418583505538\ut{sec}\\ &\approx1.83\ut{sec}\\ \end{aligned}$$ $$\ab{b}$..

문제의 유효숫자가 애매하여 다양하게 표현하였습니다. $$\begin{cases} v_1&=30\ut{m/s}\\ S_{1->2}&=160\ut{m}\\ v_2&=60\ut{m/s} \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} 2aS&=v^2-{v_0}^2,\\ \end{aligned}$$ $$ \begin{aligned} a&=\frac{v^2-{v_0}^2}{2S}\\ &=\frac{(60\ut{m/s})^2-{(30\ut{m/s})}^2}{2(160\ut{m})}\\ &=\frac{135}{16}\ut{m/s^2}\\ &=8.4375\ut{m/s^2}\\ &\approx8.4\ut{m/s^2}\\ &\approx8\ut{m/s^2}\\ \end{aligned} ..

$$\begin{cases} t &= 0.50\ut{min}\\ v_{C0} &= 15\ut{km/h}\\ v_{C1} &= 45\ut{km/h}\\ v_{B0} &= 0\\ v_{B1} &= 30\ut{km/h}\\ \end{cases}$$ $$\begin{aligned} v&=v_0+at,\\ \end{aligned}$$ $$\ab{a}$$ $$ \begin{aligned} a&=\frac{v-v_0}{t}\\ &=\frac{(45\ut{km/h})-(15\ut{km/h})}{0.50\ut{min}}\cdot\frac{60\ut{min}}{1\ut{h}} \\ &=3600\ut{km/h^2}\\ &=3600\ut{km/h^2}\cdot\frac{1000\ut{m}}{1\ut{km}}\cdot\..

$$\begin{cases} v_0 &= 3.70\times10^5\ut{m/s}\\ L &= 2.30\ut{cm}\\ v &= 4.40\times10^6\ut{m/s} \end{cases}$$ $$\begin{aligned} 2aS&=v^2-{v_0}^2,\\ \end{aligned}$$ $$ \begin{aligned} a&=\frac{(4.40\times10^6\ut{m/s})^2-{(3.70\times10^5\ut{m/s})}^2}{2(2.30\ut{cm})}\cdot\frac{100\ut{cm}}{1\ut{m}} \\ &=\frac{9611550000000000}{23}\ut{m/s^2}\\ &\approx4.1789347826086956\times 10^{14}\ut{m/s^2}\\ &..

풀이자주 : 문제의 유효숫자가 애매하여 다양하게 표현했습니다. $$\begin{cases} g &=9.80665\ut{m/s^2}\\ H &=4000\ut{m}\\ v_0 &= 0 \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} 2aS&=v^2-{v_0}^2,\\ 2(-g)(-H)&=v^2\\ \end{aligned}$$ $$ \begin{aligned} v&=\sqrt{2gH}\\ &=\sqrt{2(9.80665\ut{m/s^2})(4000\ut{m})}\\ &=\sqrt{\frac{392266}{5}}\ut{m/s}\\ &\approx 280.0949838893942\ut{m/s}\\ &\approx 2.801\times10^2\ut{m/s}\\ &\approx 2..

풀이에 필요한 정보가 너무 부족하여 고양이의 질량과 구성성분비는 임의로 정했습니다. $$\begin{cases} \text{Cat} &= 5\ut{kg}\\ 1\ut{mol}&=6.02\times10^{23}\\ 1\ut{u}&=1\ut{g/mol} \end{cases}$$ $$\begin{cases} O : 70\ut{\%}\\ C : 20\ut{\%}\\ H : 10\ut{\%}\\ \end{cases}$$ $$\begin{cases} m_O &= 16\ut{u}\\ m_C &= 12\ut{u}\\ m_H &= 1.0\ut{u}\\ \end{cases}$$ $$ \begin{cases} M_O &= 5\ut{kg}\cdot0.7=3.5\ut{kg}\\ M_C &= 5\ut{kg}\cdot0..

$$\begin{aligned} \Ans&=0.257\ut{kg/day}\\ &=0.257\ut{kg/day}\cdot\frac{10^6\ut{mg}}{1\ut{kg}}\cdot\frac{1\ut{day}}{24\ut{h}}\cdot\frac{1\ut{h}}{60\ut{min}} \\ &=\frac{6425}{36}\ut{mg/min}\\ &\approx178.47222222222223\ut{mg/min}\\ &\approx178\ut{mg/min}\\ \end{aligned}$$

$$ \begin{cases} 43\ut{cm}