7-45 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \vec F(x\ut{m})&=(cx-3.00x^2)\i\ut{N}\\ K(0)&=26.0\ut{J}\\ K(3.00\ut{m})&=11.0\ut{J} \end{cases} $$ $$W=\Delta K,$$ $$ \begin{aligned} W&=K(3)-K(0)\\ -15&=\int_{0}^{3} F \cdot \dd x\\ &=\int_{0}^{3} (cx-3x^2) \cdot \dd x\\ &=\[\frac{c}{2}x^2-x^3\]_{0}^{3}\\ &=\frac{9c}{2}-27\\ \end{aligned} $$ $$ \begin{aligned} c&=\frac{8}{3}\\ &\approx 2.6666666666666665\\ &\approx 2.67\\ \end{aligned} $$