5-20 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=14\ut{kg}\\ \vec v_0&=6.0\i\ut{m/s}\\ \vec F&=12\j\ut{N}\\ t&=3.0\ut{s} \end{cases} $$ $$ \begin{aligned} \vec a&=\frac{\vec F}{m}\\ &=\frac{12}{14}\j\ut{m/s^2}\\ &=\frac{6}{7}\j\ut{m/s^2}\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} \vec v(t) &= \vec v_0 + \int_0^t \vec a \dd t\\ &= 6\i + \int_0^t \(\frac{6}{7}\j\)\dd t\\ &= 6\i + \frac{6}{7}t\j\\ \end{aligned} $$ $$ \begin{aligned} \vec v(3)&= 6\i + \frac{6}{7}\cdot3\j\\ &= 6\i + \frac{18}{7}\j\ut{m/s}\\ &\approx 6.0\i + 2.6\j\ut{m/s}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \vec r(t) &= \vec r_0 + \int_0^t \vec v \dd t\\ &= 0 + \int_0^t \(6\i + \frac{6}{7}t\j\)\dd t\\ &= 6t\i + \frac{3}{7}t^2\j\\ \end{aligned} $$ $$ \begin{aligned} \vec r(3)&=18\i+\frac{27}{7}j\ut{m}\\ &\approx 18\i+3.9j\ut{m}\\ \end{aligned} $$