4-11 할리데이 10판 솔루션 일반물리학

$$\vec r = (3.00t^3-6.00t)\hat i +(7.00-8.00t^4)\hat j\ut{m}$$
(a) $$\begin{aligned} \vec r_3 &= (3.00\cdot 3^3-6.00\cdot 3)\hat i +(7.00-8.00\cdot 3^4)\hat j\ut{m}\\ &=63\hat i -641\hat j\ut{m} \end{aligned}$$
(b) $$\begin{aligned} \vec v =&\dxt{\vec r}\\ =& (9 t^2-6)\hat i -32 t^3\hat j\ut{m/s} \end{aligned}$$ $$\begin{aligned} \vec v_3 =&(9 \cdot 3^2-6)\hat i -32 \cdot 3^3\hat j\ut{m/s}\\ =& 75\hat i -864\hat j\ut{m/s} \end{aligned}$$
(c) $$\begin{aligned} \vec a =&\dxt{\vec v}=\dxtt{\vec r}\\ =& 18 t\hat i -96 t^2\hat j\ut{m/s^2} \end{aligned}$$ $$\begin{aligned} \vec a_3 =&18 \cdot 3\hat i -96 \cdot 3^2\hat j\ut{m/s^2}\\ =& 54 \hat i -864\hat j\ut{m/s^2} \end{aligned}$$
(d) $$\begin{aligned} \theta_{\vec v3} =& \tan^{-1}(\frac{-864}{75})\\ =&-\tan^{-1}(\frac{288}{25})\\ \approx&-1.4842078233\ut{rad}\\ \approx&-1.48\ut{rad}\\ \end{aligned}$$