2-56 할리데이 11판 솔루션 일반물리학

$$\begin{cases} R&:\text{Red Car}\\ G&:\text{Green Car}\\ t_0&:\text{Car Start}\\ t_1&:\text{Car Meet}\\ A&:\text{Case A}\\ B&:\text{Case B}\\ \end{cases}$$ $$\begin{cases} x_{R0}&=0\\ x_{G0}&=230\ut{m}\\ v_{RA}&=20.0\ut{km/h}=\frac{50}{9}\ut{m/s}\\ x_{A1}&=44.5\ut{m}\\ v_{RB}&=40.0\ut{km/h}=\frac{100}{9}\ut{m/s}\\ x_{B1}&=76.6\ut{m}\\ \end{cases}$$ $$\title{Red Car}$$ $$\begin{aligned} \Delta x_{RA}&=v_{RA} t_A\\ 44.5&=\frac{50}{9}t_A\\ t_A&=\frac{801}{100}\ut{s}\\ &=8.01\ut{s} \end{aligned}$$ $$\begin{aligned} \Delta x_{RB}&=v_{RB} t_B\\ 76.6&=\frac{100}{9}t_B\\ t_B&=\frac{3447}{500}\ut{s}\\ &=6.894\ut{s} \end{aligned}$$ $$\title{Green Car}$$ $$S=v_0t+\frac{1}{2}at^2,$$ $$\begin{cases} S_A&=v_0t_A+\frac{1}{2}a{t_A}^2\\ S_B&=v_0t_B+\frac{1}{2}a{t_B}^2\\ \end{cases}$$ $$\begin{cases} 44.5-230&=v_0(8.01)+\frac{1}{2}a(8.01)^2\\ 76.6-230&=v_0(6.894)+\frac{1}{2}a(6.894)^2\\ \end{cases}$$ $$\begin{cases} v_0&=-\cfrac{52770425}{3170091}\ut{m/s}\\ a&=-\cfrac{139175000}{85592457}\ut{m/s^2}\\ \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} v_0&=-\cfrac{52770425}{3170091}\ut{m/s}\\ &\approx-16.646343906215943\ut{m/s}\\ &\approx-16.6\ut{m/s}\\ \end{aligned}$$ $$\ab{b}$$ $$\begin{aligned} a&=-\frac{139175000}{85592457}\ut{m/s^2}\\ &\approx -1.626019451690702\ut{m/s^2}\\ &\approx -1.63\ut{m/s^2}\\ \end{aligned}$$