솔루션피아

$$\begin{cases} R&:\text{Red Car}\\ G&:\text{Green Car}\\ t_0&:\text{Car Start}\\ t_1&:\text{Car Meet}\\ A&:\text{Case A}\\ B&:\text{Case B}\\ \end{cases}$$ $$\begin{cases} x_{R0}&=0\\ x_{G0}&=230\ut{m}\\ v_{RA}&=20.0\ut{km/h}=\frac{50}{9}\ut{m/s}\\ x_{A1}&=44.5\ut{m}\\ v_{RB}&=40.0\ut{km/h}=\frac{100}{9}\ut{m/s}\\ x_{B1}&=76.6\ut{m}\\ \end{cases}$$ $$\title{Red Car}$$ $$ \begin{aligned} \De..

$$\begin{cases} t&=120\ut{ms}=0.12\ut{s}\\ v&=3400\ut{km/h}=\frac{8500}{9}\ut{m/s} \end{cases}$$ $$\begin{aligned} S&=vt\\ &=0.12\cdot\frac{8500}{9}\\ &=\frac{340}{3}\ut{m}\\ &\approx 113.3333333333333\ut{m}\\ &\approx 1.1\times10^2\ut{m}\\ \end{aligned}$$

$$\begin{cases} a&=\bra{-2(t\ut{s})+8}\ut{m/s^2}\\ v(-2.0)&=11.0\ut{m/s} \end{cases}$$ $$\begin{aligned} v&=\int a\dd t\\ &=\int (-2t+8)\dd t\\ &=-t^2+8t+C\\ \end{aligned}$$ $$\begin{aligned} v(-2)&=-(-2)^2+8(-2)+C=11\\ C&=31\\ \end{aligned}$$ $$\therefore v(t)=-t^2+8t+31$$ $$\begin{aligned} v(6.0)&=-(6)^2+8(6)+31\\ &=43\ut{m/s}\\ \end{aligned}$$

$$\begin{cases} v&=169.1\ut{km/h}=\frac{1691}{36}\ut{m/s}\\ S&=18.4\ut{m} \end{cases}$$ $$\begin{aligned} t&=\frac{S}{v}\\ &=\frac{18.4}{\frac{1691}{36}}\ut{s}\\ &=\frac{3312}{8455}\ut{s}\\ &\approx0.3917208752217622\ut{s}\\ &\approx0.392\ut{s}\\ &\approx392\ut{ms}\\ \end{aligned}$$

$$\begin{cases} t_0&:\text{Start}\\ t_1&:\text{Max Speed}\\ t_2&:\text{End}\\ \end{cases}$$ $$\begin{cases} v_{1}&=11.00\ut{m/s}\\ S_{0\rarr1}&=12.0\ut{m}\\ S_{0\rarr2}&=100\ut{m} \end{cases}$$ $$\ab{a}$$ $$S=\frac{1}{2}(v+v_0)t,$$ $$\begin{aligned} S_{0\rarr1}&=\frac{1}{2}(v_1+v_0)t_{0\rarr1}\\ &=\frac{1}{2}(11+0)t_{0\rarr1}\\ t_{0\rarr1}&=\frac{2S_{0\rarr1}}{11}\\ \end{aligned}$$ $$ \be..

$$\begin{cases} R&:\text{Red Train}\\ G&:\text{Green Train}\\ \end{cases}$$ $$\begin{cases} v_R&=72\ut{km/h}=20\ut{m/s}\\ v_G&=160\ut{km/h}=\frac{400}{9}\ut{m/s}\\ S&=950\ut{m}\\ a&=-1.0\ut{m/s^2}\\ \end{cases}$$ $$2aS=v^2-{v_0}^2,$$ $$\begin{aligned} 2(-1)S_{\text{Stop}}&=(0)^2-{v_0}^2\\ S_{\text{Stop}}&=\frac{{v_0}^2}{2}\\ \end{aligned}$$ $$ \begin{cases} S_{R\text{stop}}&=\cfrac{{v_{R0..

$$S=vt-\frac{1}{2}at^2,$$ $$\begin{cases} S_{1.5}=v_{1.5}t_{1.5}-\frac{1}{2}a_{1.5}{t_{1.5}}^2\\ S_1=v_1t_1-\frac{1}{2}a_1{t_1}^2 \end{cases}$$ $$\begin{cases} H_{1.5}=(0)t_{1.5}-\frac{1}{2}(-g){t_{1.5}}^2\\ H_1=(0)t_1-\frac{1}{2}(-g){t_1}^2 \end{cases}$$ $$\begin{cases} H_{1.5}=\frac{1}{2}g{t_{1.5}}^2\\ H_1=\frac{1}{2}g{t_1}^2 \end{cases}$$ $$ \begin{aligned} \frac{H_{1.5}}{H_1}&=\frac{..

$$\begin{cases} H&=45.0\ut{m}\\ t&=2.00\ut{s}\\ h_1&=11.8\ut{m}\\ g&=9.80665\ut{m/s^2} \end{cases}$$ $$S=vt-\frac{1}{2}at^2,$$ $$\begin{aligned} h_1-H&=v(2)-\frac{1}{2}(-g)(2)^2\\ (11.8)-(45)&=v(2)-\frac{1}{2}(-g)(2)^2\\ \end{aligned}$$ $$\begin{aligned} \abs{v}&=\abs{-\(\frac{83}{5}+g\)}\\ &=\frac{528133}{20000}\ut{m/s}\\ &=26.40665\ut{m/s}\\ &\approx 26.4\ut{m/s}\\ \end{aligned}$$

$$\begin{cases} a&=50.0\ut{m/s^2}\\ v&=80.0\ut{km/h} \end{cases}$$ $$\begin{aligned} 80\ut{km/h}&=80\ut{km/h}\cdot\frac{1000\ut{m}}{1\ut{km}}\cdot\frac{1\ut{h}}{3600\ut{s}}\\ &=\frac{200}{9}\ut{m/s} \end{aligned}$$ $$v=v_0+at,$$ $$ \begin{aligned} \frac{200}{9}\ut{m/s}&=(0)+(50\ut{m/s^2})t\\ t&=\frac{4}{9}\ut{s}\\ &\approx 0.4444444444444444\ut{s}\\ &\approx 0.444\ut{s}\\ &\approx 444\ut{ms..

$$\begin{cases} v_1&=65\ut{mi/h}\\ v_2&=70\ut{mi/h}\\ S &= 700\ut{km}\\ \end{cases}$$ $$\begin{cases} 1\ut{mile}&=5280\ut{ft}\\ 1\ut{ft}&=12\ut{in}\\ 1\ut{in}&=2.54\ut{cm}\\ \therefore 1\ut{mile}&=1.609344\ut{km} \end{cases}$$ $$ \begin{aligned} \Delta t &= t_1-t_2\\ &=\frac{S}{v_1}-\frac{S}{v_2}\\ &=S\(\frac{1}{v_1}-\frac{1}{v_2}\)\\ &=(700\ut{km})\(\frac{1}{65\ut{mi/h}}-\frac{1}{70\ut{mi/h..