A $2\mathrm{.}0-kg$ block slides across a rough surface with a constant coefficient of kinetic friction of $0\mathrm{.}50($Fig$.7-38$a$).$ The block starts at $x=0$ with an initial velocity of $4\mathrm{.}9\frac{m}{s}.$ Pushing the block is a force directed at $36\mathrm{.}8$ below the horizontal and whose magnitude increases with position as shown in Fig. $7-38$b$.($a$)$ What is the initial kinetic energy of the block? $($b$)$ How much work is done by the applied force in the first $4\mathrm{.}0$ m $?($c$)$ What is the magnitude of the friction force at $0\mathrm{.}0$ m $,$ and at $4\mathrm{.}0$ m $?($d$)$ Draw a line on the graph showing the magnitude of the friction force versus distance $x.($e$)$ What is the speed of the block at $4\mathrm{.}0$ m $?$

$($a$)$

$($b$)$

FIGURE $7-38$ Problem $100.$