A warehouse worker is pushing a $90\mathrm{.}0$ kg crate with a horizontal force of $289$ N at a speed of v $=0\mathrm{.}860$ m$/$s across the warehouse floor. He encounters a rough horizontal section of the floor that is $0\mathrm{.}75$ m long and where the coefficient of kinetic friction between the crate and floor is $0\mathrm{.}353.$

$($a$)$

Determine the magnitude and direction of the net force acting on the crate while it is pushed over the rough section of the floor.

magnitude Ndirection$---$Select$---$up$$down$$in the same direction as the motion of the crate$$in the opposite direction as the motion of the crate

$($b$)$

Determine the net work done on the crate while it is pushed over the rough section of the floor.

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$($c$)$

Find the speed of the crate when it reaches the end of the rough surface.