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

$($a$)$ Calculate the force constant of its spring if you must compress it $0\mathrm{.}110$ m to drive the $0\mathrm{.}0675$ kg plunger to a top speed of $24\mathrm{.}5$ m$/$s$.$

N$/$m

$($b$)$ What force $($magnitude$)$ must be exerted to compress the spring?

N