A single conservative force acting on a particle within a system varies as

F $=($Ax $+$ Bx$5)$ N$,$

where A and B are constants,

F

is in newtons, and x is in meters.

$($a$)$ Calculate the potential energy function U$($x$)$ associated with this force, taking

U $=0$

at

x $=0.$

$($Use any variable or symbol stated above as necessary.$)$

U$($x$)=$

$($b$)$ Find the change in potential energy as the particle moves from

x $=2\mathrm{.}10$ m

to

x $=3\mathrm{.}10$ m$.$

$($Use any variable or symbol stated above as necessary.$)$

$$U $=$

$($c$)$ Find the change in kinetic energy as the particle moves from

x $=2\mathrm{.}10$ m

to

x $=3\mathrm{.}10$ m$.$

$($Use any variable or symbol stated above as necessary.$)$

$$K $=$