7-52 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=2.00\ut{kg}\\ x&=9.0\ut{m}\\ a_s&=12\ut{m/s^2} \end{cases} $$ $$\Sigma \vec F = m\vec a,$$ $$ \begin{aligned} F_s&=24\ut{N} \end{aligned} $$ $$W_{i\rarr f}=\int_{i}^{f} \vec F \cdot \dd \vec S,$$ $$\ab{a}$$ $$ \begin{aligned} W_{0\rarr4}&=\int_{0}^{4} F \cdot \dd x\\ &=\frac{1}{2}(3+4)24\\ &=84\ut{J} \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} W_{0\rarr7}&=\int_{0}^{7} F \cdot \dd x\\ &=\frac{1}{2}(3+5)24-\frac{1}{2}(1+2)24\\ &=60\ut{J} \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} W_{0\rarr9}&=\int_{0}^{9} F \cdot \dd x\\ &=\frac{1}{2}(3+5)24-\frac{1}{2}(2+4)24\\ &=24\ut{J} \end{aligned} $$ $$\ab{d,e,f}$$ $$\Delta K=K=W,$$ $$ \begin{aligned} K&=\frac{1}{2}mv^2,\\ v&=\sqrt{\frac{2K}{m}} \end{aligned} $$ $$\ab{d}$$ $$ \begin{aligned} K_4&=W_{0\rarr4}\\ &=84\ut{J}\\ \end{aligned} $$ $$ \begin{aligned} v&=\sqrt{\frac{2K}{m}}\\ &=2\sqrt{21}\ut{m/s}\\ &\approx 9.16515138991168\ut{m/s}\\ &\approx 9.2\ut{m/s}\\ &\text{Foward} \end{aligned} $$ $$\ab{e}$$ $$ \begin{aligned} K_7&=W_{0\rarr7}\\ &=60\ut{J}\\ \end{aligned} $$ $$ \begin{aligned} v&=\sqrt{\frac{2K}{m}}\\ &=2\sqrt{15}\ut{m/s}\\ &\approx 7.745966692414834\ut{m/s}\\ &\approx 7.7\ut{m/s}\\ &\text{Foward} \end{aligned} $$ $$\ab{f}$$ $$ \begin{aligned} K_9&=W_{0\rarr9}\\ &=24\ut{J}\\ \end{aligned} $$ $$ \begin{aligned} v&=\sqrt{\frac{2K}{m}}\\ &=2\sqrt{6}\ut{m/s}\\ &\approx 4.898979485566356\ut{m/s}\\ &\approx 4.9\ut{m/s}\\ &\text{Foward} \end{aligned} $$