솔루션피아

$$ \begin{cases} x_{R0} &= 0\ut{m} \\ x_{G0} &= 220\ut{m} \\ a_G &= Const. \\ a_R &= 0 \end{cases}$$ $$ \begin{aligned} S &= vt, \\ S_{R} &= v_{R}t \\ t &= \frac{S_{R}}{v_{R}} \end{aligned} $$ $$ (\text{Case A}) $$ $$ \begin{aligned} v_{RA} &= 20.0\ut{km/h} \\ &= 20.0\ut{km/h}\frac{1000\ut{m}}{1\ut{km}}\frac{1\ut{h}}{3600\ut{s}} \\ &= \frac{50}{9}\ut{m/s} \\ \end{aligned} $$ $$A\begin{cases} v_{..

$$ \begin{cases} v_0 &= -20\ut{m/s} \\ S &= -60\ut{m} \\ g &=9.80665\ut{m/s^2} \end{cases}$$ $$t = ? $$ $$ S = v_0t+\frac{1}{2}at^2, $$ $$ \begin{aligned} \\ S &= v_0t+\frac{1}{2}(-g)t^2 \\ -60 &= -20t-\frac{1}{2}(9.80665)t^2 \\ t&=\frac{400 \left(-1000\pm \sqrt{3941995}\right)}{196133}\ut{s} \\ &=\frac{400 \left(-1000+ \sqrt{3941995}\right)}{196133}\ut{s} \ (\because t \ge 0) \\ &\approx 2.0097..

$$ \begin{aligned} v_0 &= 1020\ut{km/h} \\ &= 1020\ut{km/h}\cdot\frac{1000\ut{m}}{1\ut{km}}\cdot\frac{1\ut{h}}{3600\ut{s}} \\ &= \frac{850}{3}\ut{m/s} \end{aligned} $$ $$ \begin{cases} v_0 &= \frac{850}{3}\ut{m/s} \\ t &= 1.4\ut{s} \\ v &= 0 \\ g &=9.80665\ut{m/s^2} \end{cases}$$ $$ \frac{a}{g} = ? $$ $$ v=v_0+at, $$ $$ \begin{aligned} \frac{a}{g}&= \frac{v-v_0}{gt} \\ &= \frac{-(\frac{850}{3}\u..

$$ \begin{cases} v_0 &= 0 \\ x_0 &= 0 \\ x_1 &= 0.500\ut{km} = 500\ut{m} \\ a_{0\to1} &= 10.0\ut{m/s^2} \\ g &=9.80665\ut{m/s^2 } \end{cases}$$ $$\max x= x_M=?$$ $$\begin{aligned} 2aS &= v^2-v_0^2, \\ 2a_{0\to1}x_{0\to1}&= v_1^2-v_0^2 \end{aligned} $$ $$ \begin{aligned} v_1 &= \sqrt{2a_{0\to1}x_{0\to1}} \ (\because v_0=0) \\ &= \sqrt{2(10.0\ut{m/s^2})(500\ut{m})} \\ &=100\ut{m/s} \end{aligned} $..

$$ \begin{aligned} v_0 &= 146\ut{km/h} \\ &= 146\ut{km/h}\cdot\frac{1000\ut{m}}{1\ut{km}}\cdot\frac{1\ut{h}}{3600\ut{s}} \\ &= \frac{365}{9}\ut{m/s} \end{aligned}$$ $$ \begin{aligned}\\ v &= 90\ut{km/h} \\ &= 90\ut{km/h}\cdot\frac{1000\ut{m}}{1\ut{km}}\cdot\frac{1\ut{h}}{3600\ut{s}} \\ &= 25\ut{m/s} \end{aligned}$$ $$ \begin{cases} a &= -5.2\ut{m/s^2} \\ v_0 &= \frac{365}{9}\ut{m/s} \\ v &= 25\u..

$$\begin{aligned} \max v &= 305\ut{m/min} \\ &= 305\ut{m/min}\frac{1\ut{min}}{60\ut{s}} \\ &= \frac{61}{12}\ut{m/s} \end{aligned}$$ $$ \begin{cases} \max v &= v_M=\frac{61}{12}\ut{m/s} \\ \max S &= S_M=190 \ut{m} \\ |a| &= 1.22\ut{m/s^2} \\ v_0 &= 0 \end{cases} $$ (a) $$ S_a =? $$ $$ 2aS = v^2-v_0^2, $$ $$\begin{aligned} S_a &= \frac{v_M^2}{2a}(\because v_0=0) \\ &= \frac{(\frac{61}{12}\ut{m/s})..

$$ \begin{cases} a = -4.92 \ut{m/s^2} \\ v_0 = 27.2 \ut{m/s} \\ v = 0 \end{cases}$$ (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_..

$$ \begin{cases} v_0 &= 0 \\ a &= \Cons \\ t &= 5.00\ut{ms} = 0.005\ut{s} \\ S &= 2.00\ut{cm} = 0.02\ut{m} \end{cases} $$ $$ a =? $$ $$\begin{aligned} S &= v_0t+\frac{1}{2}at^2 \\ &= \frac{1}{2}at^2 (\because v_0=0) \end{aligned} $$ $$ \begin{aligned} \Ans &= a = \frac{2S}{t^2} \\ &=\frac{2(0.02\ut{m})}{(0.005\ut{s})^2} \\ &= 8.00\ut{m/s} \end{aligned} $$

$$ \begin{cases} v_0 &= 6.00\times10^6\ut{m/s} \\ a &= -1.25\times10^{14}\ut{m/s^2} \\ v &= 0 \end{cases} $$ (a) $$ S =? $$ $$ 2aS = v^2-v_0^2 ,$$ $$ \begin{aligned} \Ans &= S = \frac{v^2-v_0^2}{2a} \\ &= \frac{0^2-(6.00\times10^6\ut{m/s})^2}{2(-1.25\times10^{14}\ut{m/s^2})} \\ &= \frac{18}{125}\ut{m} \\ &= 0.144\ut{m} = 14.4\ut{cm} \end{aligned} $$ (b) $$ \begin{aligned} x(t) &= v_0t+\frac{1}{2..

$$ \begin{cases} t&=2.5\ut{s} \\S &= 8.0\ut{m}-2.0\ut{m} = 6.0\ut{m} \\ v_0 &= 2.8\ut{m/s} \\ a &= \Cons \end{cases} $$ $$a=? $$ $$ S = v_0t+\frac{1}{2}at^2 $$ $$ \begin{aligned} \\ \Ans &= a = \frac{2(S-v_0t)}{t^2} \\ &= \frac{2\{6.0\ut{m}-(2.8\ut{m/s})(2.5\ut{s})\}}{(2.5\ut{s})^2} \\ &= -\frac{8}{25}\ut{m/s^2} \\ &= -0.32\ut{m/s^2} \end{aligned} $$