4-14 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec v_0 &= 4.0\i-2.0\j+3.0\k\ut{m/s}\\ \vec v_{4.0} &= -2.0\i-2.0\j+5.0\k\ut{m/s}\\ \end{cases}$$
(a) $\vec a_{avg}=?$ $$\begin{aligned} \vec a_{avg} &= \frac{\Delta \vec v}{\Delta t}\\ &=\frac{\vec v_4-\vec v_0}{4}\\ &=\frac{(-2.0\i-2.0\j+5.0\k)-(4.0\i-2.0\j+3.0\k)}{4}\ut{m/s^2}\\ &=-1.5\i+0.5\k\ut{m/s^2}\\ \end{aligned}$$
(b) $\abs{\vec a_{avg}}=?$ $$\begin{aligned} \abs{\vec a_{avg}} &= \sqrt{(-1.5)^2+(0.5)^2}\ut{m/s^2}\\ &=\sqrt{\frac{5}{2}}\ut{m/s^2}\\ &\approx1.58113883008\ut{m/s^2}\\ &\approx1.6\ut{m/s^2}\\ \end{aligned}$$
(c) $\theta_{\vec a}=?$ $$\begin{aligned} \theta_{\vec a} &= \cos^{-1}\(\frac{a_x}{\abs{\vec a}}\)\\ &=\cos^{-1}\(-\frac{3}{\sqrt{10}}\)\\ &\approx2.81984209919\ut{rad}\\ &\approx2.8\ut{rad}\\ \end{aligned}$$