2-67 할리데이 10판 솔루션 일반물리학

$$\begin{cases} A = \text{No Helmat}\\ B = \text{Helmat}\\ \end{cases}$$ $$\abs{\max v_A -\max v_B} =?$$ $$\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\\ =&\(\int_0^{0.002}a_A\dd t+\int_{0.002}^{0.004}a_A\dd t+\int_{0.004}^{0.006}a_A\dd t+\int_{0.006}^{0.007}a_A\dd t\)\\ &-\(\int_0^{0.003}a_B\dd t+\int_{0.003}^{0.004}a_B\dd t+\int_{0.004}^{0.006}a_B\dd t+\int_{0.006}^{0.007}a_B\dd t\)\\ =&\[\bra{\int_0^{0.002}a_A\dd t+\int_{0.002}^{0.004}a_A\dd t}-\bra{\int_0^{0.003}a_B\dd t+\int_{0.003}^{0.004}a_B\dd t}\]\\ &+\[\int_{0.004}^{0.006}(a_A-a_B)\dd t+\int_{0.006}^{0.007}(a_A-a_B)\dd t\]\\ =&\[\bra{\frac{1}{2}\cdot 0.002\cdot 120+\frac{1}{2}\cdot 0.002\cdot (120+140)}-\frac{1}{2}\cdot (0.004+0.001)\cdot 20\]\\ &+\[\frac{1}{2}\cdot 0.002\cdot (100+120)+\frac{1}{2}\cdot 0.001\cdot 120\]\\ =&\frac{61}{100}\ut{m/s}\\ =&0.61\ut{m/s}\\ \end{aligned}$$