솔루션피아

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

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

$$ \begin{aligned} \\ S &= 1.0\ut{mm}-5.0\ut{\mu m} \\ &= 1.0\ut{mm}\frac{1\ut{m}}{10^3\ut{mm}}-5.0\ut{\mu m}\frac{1\ut{m}}{10^6\ut{\mu m}} \\ &= \frac{199}{200000}\ut{m} \\ &= 9.95\times 10^{-4}\ut{m} \end{aligned} $$ $$ \begin{cases} v_0 &= 1.6\ut{m/s} \\ S &= 9.95\times 10^{-4}\ut{m} \\ v &= 0 \\ a &= Const. \\ g &= 9.80665 \ut{m/s^2} \end{cases} $$ (a) t=? $$S = \frac{1}{2}(v+v_0)t ,$$ $$ \b..

$$ \begin{cases} v_0 &= 0 \\ a &= \Cons \\ t_A &= \frac{1}{5}\ut{s} \\ t_B &= 5.00\ut{s} \end{cases} $$ $$ \Ans = S_A : S_B =?$$ $$\begin{aligned} \\ S &= v_0t+\frac{1}{2}at^2 \\ &= \frac{1}{2}at^2 (\because v_0=0) \end{aligned} $$ $$ \begin{aligned} \Ans &= S_A : S_B \\ &= \frac{1}{2}at_A^2 : \frac{1}{2}at_B^2 \\ &= t_A^2 : t_B^2 \\ &= \left(\frac{1}{5}\ut{s}\right)^2 : (5.00\ut{s})^2 \\ &= 1:6..

$$x= ct^2 - bt^3$$ (a) $$ \Ans = c =? $$ $$ \put k_n = \text{AnyNumber} $$ $$\begin{aligned} x &= ct^2 - bt^3=k_1\ut{m} \\ &\Rightarrow c(t\ut{s})^2 - b(t\ut{s})^3 = k_1\ut{m} \cdots(2-22-1) \\ &\Rightarrow c(t\ut{s})^2 = k_2\ut{m} \\ &\Rightarrow c(t^2\ut{s^2}) = k_2\ut{m} \\ &\Rightarrow c = \frac{k_2\ut{m}}{t^2\ut{s^2}} \\ &\Rightarrow c = \frac{k_2}{t^2}\ut{m/s^2} \end{aligned} $$ (b) $$ \An..

$$ \begin{aligned} v_0 &= 130\ut{km/h} \\&= 130\ut{km/h}\cdot\frac{1000\ut{m}}{1\ut{km}}\cdot\frac{1\ut{h}}{3600\ut{s}} \\ &= \frac{325}{9}\ut{m/s} \end{aligned} $$ $$ \begin{cases} v_0 &= \frac{325}{9}\ut{m/s} \\ v &= 0 \\ S &= 210\ut{m} \\ a &= \Cons \end{cases} $$ (a) $$\Ans = \abs{a} =? $$ $$2aS = v^2-v_0^2, $$ $$ \begin{aligned} \Ans &= \abs{a} = \abs{\frac{v^2-v_0^2}{2S}} \\ &= \abs{\frac{..

$$ x = 25t-6.0t^3 $$ $$ \begin{aligned} v &= \dot x = \frac{dx}{dt} \\ &= \frac{d}{dt}(25t-6.0t^3) \\ &= 25-18 t^2 \end{aligned} $$ $$ \begin{aligned} a &= \dot v = \frac{dv}{dt} \\ &= \frac{d}{dt}(25-18 t^2) \\ &= -36 t \end{aligned} $$ $$ \therefore \begin{cases} x &= 25t-6.0t^3 \\ v &= 25-18 t^2 \\ a &= -36 t \end{cases}\cdots(2-20-1) $$ (a) $$\Ans =t_{v=0} = ? $$ $$ (2-20-1), $$ $$v = 25-18 ..