2-12 할리데이 10판 솔루션 일반물리학

$$\begin{cases} v_s &= 5.00\ut{m/s} \\ v &= 25.0\ut{m/s} \\ L &= 12.0\ut{m} \end{cases} $$
(a) $$ \put \begin{cases} x &= \text{Wave End Point} \\ L_a &= \text{Added Wave Length} \\ n &= \text{Number Of Added Cars} \\ t_a &= \text{Time Of Add 1 Car} \end{cases} $$ $$ \begin{aligned} t_a &= \frac{d}{v-v_s} \\ t &= nt_a \\ n &= \frac{t}{t_a} = t\frac{v-v_s}{d} \end{aligned} $$ $$ \begin{aligned} x &= \Delta x - L_a \\ &= v_st - nL \\ &= v_st - Lt\frac{v-v_s}{d} \\ &= \left(v_s - L\frac{v-v_s}{d}\right)t \end{aligned} $$ $$ \begin{aligned} \dot x &= \dxt{x} \\ &= \dt\left(v_s - L\frac{v-v_s}{d}\right)t \\ &= v_s - L\frac{v-v_s}{d} = 0 \cdots({2-12-1}) \end{aligned} $$ $$ \begin{aligned} v_s &= L\frac{v-v_s}{d} \\ d &= \frac{L(v-v_s)}{v_s} \\ &= L\left(\frac{v}{v_s}-1\right) \\ &= 12.0\ut{m}\left(\frac{25.0\ut{m/s}}{5.00\ut{m/s} }-1\right) \\ &= 48.0\ut{m} \end{aligned} $$
(b) $$ \begin{aligned} d_2 &= 2d \\ &({2-12-1}), \\ \dot x &= v_s - L\frac{v-v_s}{d} \\ &= 5.00\ut{m/s} - 12.0\ut{m}\frac{25.0\ut{m/s}-5.00\ut{m/s}}{2\cdot 48.0\ut{m}} \\ &= +2.50\ut{m/s} \\ &\(\text{+ means right direction} \) \end{aligned} $$