4-16 할리데이 10판 솔루션 일반물리학

$$\vec v = (6.0t-4.0t^2)\i+8.0\j\ut{m/s}$$
(a) $\vec a_{2.5}=?$ $$\begin{aligned} \vec a &= \dxt{\vec v}\\ &= \dt\{(6.0t-4.0t^2)\i+8.0\j\}\\ &= (6-8t)\i\ut{m/s^2}\\ \end{aligned}$$ $$\begin{aligned} \vec a_{t=2.5}&=(6-8\cdot2.5)\i\ut{m/s^2}\\ &=-14\i\ut{m/s^2} \end{aligned}$$
(b) $t_{a=0}=?$ $$\vec a = (6-8t)\i=0$$ $$\begin{aligned} t&=\frac{3}{4}\ut{s}\\ &= 0.75\ut{s} \end{aligned}$$
(c) $t_{v=0}=?$ $$v = \sqrt{(6.0t-4.0t^2)^2+8.0^2}=0$$ $$\title{Impossible}$$
(d) $t_{v=10}=?$ $$v = \sqrt{(6.0t-4.0t^2)^2+8.0^2}=10$$ $$\begin{aligned} t&=\frac{1}{4} \left(3+\sqrt{33}\right)\ut{s}(\because t>0)\\ &\approx2.186140661634507\ut{s}\\ &\approx2.2\ut{s}\\ \end{aligned}$$