8-13 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=1700\ut{kg}\\ t&=30\ut{s}\\ v&=82\ut{km/h}=\frac{205}{9}\ut{m/s} \end{cases} $$ $$\ab{a}$$ $$\KE=\frac{1}{2}mv^2,$$ $$ \begin{aligned} \KE&=\frac{1}{2}\cdot 1700 \cdot \(\frac{205}{9}\)^2\\ &=\frac{35721250}{81}\ut{J}\\ &\approx 441003.0864197531\ut{J}\\ &\approx 4.4 \times 10^5 \ut{J}\\ &\approx 0.44 \ut{MJ}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} P&=\frac{W}{t}\\ &=\frac{\Delta \KE}{t}=\frac{\KE}{t}\\ &=\frac{\frac{35721250}{81}}{30}\\ &=\frac{3572125}{243}\ut{W}\\ &\approx 14700.102880658436\ut{W}\\ &\approx 1.5\times10^4\ut{W}\\ &\approx 15\ut{kW}\\ \end{aligned} $$ $$\ab{c}$$ $$v=v_0+at,$$ $$ \begin{aligned} a&=\frac{\Delta v}{t}\\ &=\frac{\frac{205}{9}}{30}\\ &=\frac{41}{54}\ut{m/s^2} \end{aligned} $$ $$ \begin{aligned} P&=F\cdot v\\ &=ma\cdot v\\ &=1700 \cdot \frac{41}{54} \cdot \frac{205}{9}\\ &=\frac{7144250}{243}\ut{W}\\ &\approx 29400.205761316873\ut{W}\\ &\approx 2.9\times 10^4\ut{W}\\ &\approx 29\ut{kW}\\ \end{aligned} $$