솔루션피아

$$ x = 16te^{-t} $$ $$ \Ans = \abs{x(t_{\dot x=0})} =? $$ $$ \begin{aligned} \dot x &= \dxt{x} \\&= \dt(16te^{-t}) \\&= 16 e^{-t}-16 te^{-t} \\&= -16 e^{-t} (t-1) = 0 \end{aligned} $$ $$ t=1\ut{s} $$ $$ \begin{aligned} \\\abs{x(1)} &= \abs{16(1)e^{-(1)}} \\ &= \frac{16}{e}\ut{m} \\&\approx 5.886071058743077\ut{m} \end{aligned} $$

(a) $$ \begin{cases} v_1 &= 55\ut{km/h} \\ v_2 &= 90\ut{km/h} \\ t &= t_1 = t_2 \end{cases} $$ $$ \begin{aligned} \Ans &= \bar v_a = \frac{\Sigma S}{\Sigma t} =\frac{S_1+S_2}{t_1+t_2} \\ &=\frac{S_1+S_2}{2t} \\ &=\frac{1}{2}\left(\frac{S_1}{t}+\frac{S_2}{t}\right) \\ &=\frac{v_1+v_2}{2} \\ &=\frac{55\ut{km/h}+90\ut{km/h}}{2} \\ &=72.5\ut{km/h} \\ &\approx 73\ut{km/h} \end{aligned} $$ (b) $$ \beg..

$$\begin{cases} v_s &= 5.00\ut{m/s} \\ v &= 25.0\ut{m/s} \\ L &= 12.0\ut{m} \end{cases} $$ (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..

$$ \begin{cases} v_c &= 15.00\ut{m/s} \\ t &= 150.0\ut{s} \\ x_{c0}-x_{a0} &= 1.500\ut{km} \end{cases} $$ $$ \begin{aligned} \Ans &= v_a = ? \\ x_{c0}+\Delta x_c &= x_{a0}+\Delta x_a \\ x_{c0}-x_{a0} &= \Delta x_a-\Delta x_c \\ &= v_at-v_ct \\ &= (v_a-v_c)t \\ v_a-v_c&= \frac{x_{c0}-x_{a0}}{t} \\ v_a&= \frac{x_{c0}-x_{a0}}{t}+v_c \\ &= \frac{1.500\ut{km}}{150.0\ut{s}}\cdot\frac{1000\ut{m}}{1\ut{..

(a) $$ \begin{aligned} \\ v_{e1} &= \frac{v_1 + v_2}{2}= \frac{\frac{d}{t_1}+\frac{d}{t_2}}{2} \\ &= \frac{d}{2} \left( \frac{1}{t_1}+\frac{1}{t_2}\right) \\ &= \frac{d}{2} \frac{t_1+t_2}{t_1t_2} \\ &= \frac{d(t_1+t_2)}{2t_1t_2}\ne v_e \end{aligned} $$ $$ \begin{aligned} \\ v_{e2} &= \frac{d}{\bar t}= \frac{d}{\frac{t_1+t_2}{2}} \\ &= \frac{2d}{t_1+t_2} \cdots({2-10-1} ) \\ &= \frac{d_1+d_2}{t_1..

($L_1=1\ut{km}$ 로 추정함.) $$ \begin{cases} S &= 1\ut{km} \\ t_1 &= 2\ut{min}+27.95\ut{s} = 147.95\ut{s} \\ t_2 &= 2\ut{min}+28.15\ut{s} = 148.15\ut{s} \\ L_2 &= L_1 + \Delta L \\ v_1 &> v_2 \end{cases} $$ $$ \begin{aligned} v_1 &> v_2 \\ \frac{L_1}{t_1} &> \frac{L_2}{t_2} \\ \frac{L_1}{t_1} &> \frac{L_1 + \Delta L}{t_2} \\ \frac{L_1}{t_1} &> \frac{L_1}{t_2}+\frac{\Delta L}{t_2} \\ \\ \frac{\Delta ..

$$ \begin{cases} v_w &= 3.50\ut{m/s} \\ d &= 0.25\ut{m} \\ L &= 1.75\ut{m} \end{cases} $$ (a) $$ \put \begin{cases} n &= \text{Human On Wall Number}\ut{EA} \\ t_k &= \text{Human k to Wall Time}\ut{s} \\ t &= \text{Overall Time}\ut{s} \end{cases} $$ $$ \begin{cases} t_1 &= \frac{L}{v_w} \\ t_2 &= t_1 + \frac{L}{v_w} \\ t_3 &= t_2 + \frac{L}{v_w} \\ \vdots \\ \Delta t &= \frac{L}{v_w} \end{cases} ..

$$ \begin{aligned} & \begin{cases} S_0 &= 40\ut{km} \\ \abs{v_{\text{BIRD}}} &= 36\ut{km/h} \\ v_A &= 16\ut{km/h} \\ v_B &= -25\ut{km/h} \end{cases}\\ \end{aligned} $$ (a) $$ \begin{aligned} \\ \Ans &= \Sigma\abs{S_{\text{BIRD}}} = ? \\ &= \Sigma\abs{v_{\text{BIRD}} \cdot t_{\text{BIRD}}} \\ &=\abs{v_{\text{BIRD}}}\cdot \Sigma\abs{t_{\text{BIRD}}} \\ &=\abs{v_{\text{BIRD}}}\cdot t_{\text{CARCRAS..

$$ \begin{cases} S &= 200\ut{m} \\ t &= 6.509\ut{s} \\ \Delta v &= 19\ut{km/h} \end{cases} $$ $$ \begin{aligned} & \\ \Ans &= t = ? \\&= \frac{S}{v} = \frac{S}{v_0+\Delta v} \\&= \frac{S}{\frac{S}{t}+\Delta v} \\&= \frac{200\ut{m}}{\frac{200\ut{m}}{6.509\ut{s}}+19\ut{km/h}\cdot \frac{1000\ut{m}}{1\ut{km}}\cdot \frac{1\ut{h}}{3600\ut{s}}} \\&= \frac{4686480}{843671}\ut{s} \\&\approx 5.55486676678..

(a) t=1s $$ x(1) = 3(1) - 4(1)^2 + (1)^3= 0\ut{m}$$ (b) t=2s $$ x(2) = 3(2) - 4(2)^2 + (2)^3= -2\ut{m} $$ (c) t=3s $$ x(3) = 3(3) - 4(3)^2 + (3)^3= 0\ut{m} $$ (d) t=4s $$ x(4) = 3(4) - 4(4)^2 + (4)^3= 12\ut{m} $$ (e) $$ \begin{aligned} \Ans &= \Delta x = x(4)-x(0) \\ &= 12\ut{m}- \bra{3(0) - 4(0)^2 + (0)^3} \\ &= 12\ut{m} \end{aligned} $$ (f) $$ \begin{aligned} \Ans &= \frac{\Delta x}{\Delta t} ..