8-46 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} m&=17.0\ut{kg}\\ a&=2.50\ut{m/s^2}\\ v_i&=14.0\ut{m/s}\\ v_f&=34.0\ut{m/s}\\ \end{cases} $$ $$ \put \begin{cases} \KE : \text{Kinetic Energy}\\ \GE : \text{Gravitational Potential Energy}\\ \ME : \text{Mechanical Energy}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \Delta \ME&=\Delta \KE+\Delta \GE\\ &=\Delta \KE\\ &=\Delta \(\frac{1}{2}mv^2\)\\ &=\frac{1}{2}m\Delta \(v^2\)\\ &=\frac{1}{2}m \({v_f}^2-{v_i}^2\)\\ &=8160\ut{J}\\ &=8.16\ut{kJ} \end{aligned} $$ $$\ab{b}$$ $$v=v_0+at,$$ $$ \begin{aligned} t&=\frac{v_f-v_i}{a}\\ \end{aligned} $$ $$ \begin{aligned} P&=\frac{\Delta E}{t}\\ &=\frac{\frac{1}{2}m \({v_f}^2-{v_i}^2\)}{\frac{v_f-v_i}{a}}\\ &=ma\cdot\frac{v_i+v_f}{2}\\ &=1020\ut{W}\\ &=1.02\ut{kW}\\ \end{aligned} $$ $$\ab{cd}$$ $$\Sigma F = ma,$$ $$ P(v)=Fv=mav $$ $$\ab{c}$$ $$ P(14)=595\ut{W}$$ $$\ab{c}$$ $$ P(34) = 1445\ut{W} \approx 1.45\ut{kW} $$