One type of BB gun uses a spring$-$driven plunger to blow the BB from its barrel.

$($a$)$

Calculate the force constant $($in N$/$m$)$ of its plunger's spring if you must compress it $0\mathrm{.}140$ m to drive the $0\mathrm{.}0440$ kg plunger to a top speed of $22\mathrm{.}0$ m$/$s$.$

N$/$m

$($b$)$

What force $($in N$)$ must be exerted to compress the spring? $($Enter the magnitude.$)$

N

s