Question

A box of books weighing 280 N is shoved across the floor of an apartment by a force of 390 N exerted downward at an angle of 35.1° below the horizontal. If the coefficient of kinetic friction between box and floor is 0.57, how long does it take to move the box 4.00 m, starting from rest?

Answer 1

Figuring the pushing force as horizontal and vertical forces is the first key. the horizontal component makes it move, the vertical force adds downward force increasing friction.

frictionforce=mu*forcenormal
= mu*(Weight+290sintheta)
Netforcemoving force=horizontalpushing-friction
= 290*cosTheta-mu(Weight-290sinTheta)
but you know acceleration= netpushingforce/mass

so solve for a.

Then
distance=1/2 a*t^2 solve for t.