2-28 할리데이 10판 솔루션 일반물리학

$$\begin{cases} a = -4.92 \ut{m/s^2} \\ v_0 = 27.2 \ut{m/s} \\ v = 0 \end{cases}$$
(a) $$t =?$$ $$v = v_0+at = 0(\because v=0)$$ $$\begin{aligned} \\ t &= -\frac{v_0}{a} \\ &= -\frac{27.2 \ut{m/s}}{-4.92 \ut{m/s^2}} \\ &= \frac{680}{123}\ut{s} \\ &\approx 5.528455284552845\ut{s} \\ &\approx 5.53\ut{s} \end{aligned}$$
(b) $$S = ?$$ $$2aS = v^2-v_0^2,$$ $$\begin{aligned} S &= -\frac{v_0^2}{2a}(\because v=0) \\ &= -\frac{(27.2 \ut{m/s})^2}{2(-4.92 \ut{m/s^2})} \\ &= \frac{9248}{123}\ut{m} \\ &\approx 75.1869918699187\ut{m} \\ &\approx 75.2\ut{m} \end{aligned}$$
(c) $$\begin{aligned} x(t) &= v_0t+\frac{1}{2}at^2 \\ &= (27.2)t+\frac{1}{2}(-4.92)t^2 \\ &= \frac{136}{5}t-\frac{123 }{50}t^2 \end{aligned}$$ $$\begin{aligned} v(t) &= \dot x = \dxt{x} \\ &= \dt(\frac{136}{5}t-\frac{123 }{50}t^2) \\ &= \frac{136}{5}-\frac{123}{25}t \end{aligned}$$