7-54 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=10\ut{kg}\\ x_i&=0\\ x_f&=8.0\ut{m} \end{cases} $$ $$ \begin{cases} a(0\ut{m})&=0\\ a(8\ut{m})&=40.0\ut{m/s^2}\\ \end{cases} $$ $$ \begin{aligned} a(x\ut{m})&=\frac{40}{8}x\\ &=5x\ut{m/s^2} \end{aligned} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{aligned} F&=10\cdot5x\\ &=50x \end{aligned} $$ $$W_{i\rarr f}=\int_{i}^{f} \vec F \cdot \dd \vec S,$$ $$ \begin{aligned} W&=\int_{i}^{f} 50x \cdot \dd x\\ &=\[25x^2\]_{0}^{8}\\ &=1600\ut{J}\\ &=1.6\times10^3\ut{J}\\ &=1.6\ut{kJ} \end{aligned} $$