솔루션피아

$$\begin{cases} \text{Particle 1}=A\\ \text{Particle 2}=B\\ \end{cases}$$ $$\begin{cases} x_A=6 .00t^2 + 3 .00t + 2.00\\ a_B=-8.00t\\ v_B(0)=15\ut{m/s}\\ \end{cases}$$ $$v_A(k)=v_B(k) =?$$ $$\begin{aligned} v_A(t)&=\dot{x}_A=\dxt{x_A}\\ &=\dt(6 .00t^2 + 3 .00t + 2.00)\\ &=12t+3 \end{aligned}$$ $$ \begin{aligned} v_B(t)&=\int_0^ta\dd t\\ &=\int(-8.00t)\dd t\\ &=-4t^2+C\\ &=-4t^2+15 \ (\becau..

$$x(16)-x(0) =?$$ $$\begin{aligned} \Ans &= \int_0^{16}v\dd t\\ &= \int_0^2v\dd t+\int_2^{10}v\dd t+\int_{10}^{12}v\dd t+\int_{12}^{16}v\dd t\\ &=\frac{1}{2} \cdot 2 \cdot 8 + 8 \cdot 8+\frac{1}{2} \cdot 2 \cdot (8+4)+4\cdot4\\ &= 100\ut{m} \end{aligned}$$

$$v(40) =?$$ $$\begin{aligned} \Ans &= \int_0^{\frac{40}{1000}}a\dd t\\ &= \int_{\frac{10}{1000}}^{\frac{20}{1000}}a\dd t+\int_{\frac{20}{1000}}^{\frac{30}{1000}}a\dd t+\int_{\frac{30}{1000}}^{\frac{40}{1000}}a\dd t\\ &=\frac{1}{2}\cdot0.01\cdot100+\frac{1}{2}\cdot0.01\cdot(100+400)+\frac{1}{2}\cdot0.01\cdot400\\ &=5\ut{m/s} \end{aligned}$$

$$\begin{cases} A = \text{No Helmat}\\ B = \text{Helmat}\\ \end{cases}$$ $$\abs{\max v_A -\max v_B} =?$$ $$ \begin{aligned} \Ans =&\max v_A -\max v_B \ (\because v_A > v_B)\\ =&v_A(0.007) - v_B(0.007) \ (\because a_A,a_B>0)\\ =&\int_0^{0.007}a_A\dd t-\int_0^{0.007}a_B\dd t\\ =&\(\int_0^{0.002}a_A\dd t+\int_{0.002}^{0.004}a_A\dd t+\int_{0.004}^{0.006}a_A\dd t+\int_{0.006}^{0.007}a_A\dd t\)\\ &-..

(풀이자주:문제에 있는 $v_s=8.0\ut{m}$는 오타로 추정됩니다. 아마 (m/s)를 의도한 것으로 보입니다.) $$\begin{cases} v(0)=0\\ v(10)=2.0\ut{m/s}\\ v(50)=4.0\ut{m/s}\\ \end{cases}$$ (a)$\Delta x_{0\to50}=?$ $$ \begin{aligned} x(50)-x(0)&=\int^{\frac{50}{1000}}_{0}v\dd t\\ &=\int_{0}^{\frac{10}{1000}}v\dd t+\int_{\frac{10}{1000}}^{\frac{50}{1000}}v\dd t\\ &=\frac{1}{2}\cdot \frac{10}{1000} \cdot 2 + \frac{1}{2} \cdot \frac{40}{1000..

$$\begin{cases} A=\text{Head}\\ B=\text{Body}\\ \end{cases}$$ (a)$v_{A160}=?$ $$\begin{cases} v_0=0\\ a_A = \text{Linear} & \\ a_A(t) = 0 &(t

$$\begin{cases} x_1=0\\ t_1=3.0\ut{s}\\ v_0=-10\ut{m/s}\\ a=-g = -9.80665\ut{m/s^2}\\ \end{cases}$$ $$x_0=?$$ $$\begin{aligned} \Delta x &= v_0t+\frac{1}{2}at^2,\\ x_1-x_0&= (-10)(3.0)+\frac{1}{2}(-g)(3.0)^2\\ x_0&= 30+\frac{9}{2} g\\ &= 30+\frac{9}{2}(9.80665)\\ &=\frac{2965197}{40000}\ut{m}\\ &=74.1299\ut{m}\\ &\approx 74\ut{m}\\ \end{aligned}$$

$$\begin{cases} t_1 = \text{FlowerPot is Bottom of Window}\\ t_2 = \text{FlowerPot is Top of Window}\\ t_3 = \text{FlowerPot is Top Point}\\ \end{cases}$$ $$\begin{cases} x_0=0\\ x_{1\to2}=2.00\ut{m}\\ t_{1\to2}=0.50\ut{s}\\ v_3=0\\ a=-g = -9.80665\ut{m/s^2}\\ \end{cases}$$ $$x_{2\to3}=?$$ $$\Delta x = vt-\frac{1}{2}at^2,$$ $$\Delta x_{1\to2} = v_2t_{1\to2}-\frac{1}{2}(-g)t_{1\to2}^2$$ $$ ..

$$\begin{cases} t_1 = \text{Man is 15cm From Bottom 1st Time}\\ t_2 = \text{Man is Under 15cm From Top 1st Time}\\ t_3 = \text{Man is Top Point}\\ t_4 = \text{Man is Under 15cm From Top 2st Time}\\ t_5 = \text{Man is 15cm From Bottom 2nd Time}\\ t_6 = \text{Man is Landing}\\ \end{cases}$$ $$\begin{cases} x_0=x_6=0\\ x_3=0.780\ut{m}\\ v_3=0\\ x_1=x_5=0.150\ut{m}\\ x_2=x_4=x_3-0.150\ut{m}\\ a=-g..

$$\begin{cases} t_0 = \text{Ball is Top of Building}\\ t_1 = \text{DownBall is Top of Window}\\ t_2 = \text{DownBall is Bottom of Window}\\ t_3 = \text{Ball is Contact Road}\\ t_4 = \text{UpBall is Bottom of Window}\\ t_5 = \text{UpBall is Top of Window}\\ \end{cases}$$ $$\begin{cases} \Delta t_{1\to2}=0.125\ut{s}\\ \Delta t_{4\to5}=0.125\ut{s}\\ \Delta t_{2\to4}=2.00\ut{s}\\ x_0=h\\ x_{1\to2}..