A single conservative force acts on a

$5\mathrm{.}00$

$-$kg particle within a system due to its interaction with the rest of the system. The equation

$$

$$

$=$

$2$

$$

$+$

$4$

describes the force, where

$$

$$

is in newtons and

$$

is in meters. As the particle moves along the

$$

axis from

$$

$=$

$1\mathrm{.}00$

$$

m

to

$$

$=$

$5\mathrm{.}00$

$$

m

$,$ calculate

$($a$)$

the work done by this force on the particle,

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$($b$)$

the change in the potential energy of the system, and

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$($c$)$

the kinetic energy the particle has at

$$

$=$

$5\mathrm{.}00$

$$

m

if its speed is

$3\mathrm{.}00$

m$/$s at

$$

$=$

$1\mathrm{.}00$

$$

m

$.$

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