A box of books weighing 315 N is shoved across the floor by a force of 477 N exerted downward at an angle of 35° below the horizontal. If the coefficient of kinetic friction between the box and the floor is 0.58, how long does it take to move the box 4.20 m starting from rest?

It takes 1.14 s to move the box 4.20 m.

Explanation:

Using Newton's second law we have:

F is the force exerted and m the mass of the books

So, the books accelerate at:

We know that the initial velocity is zero, so using the kinematic position equation, we have:

So, we just need to solve the equation for t.

Taking the positive value of t:

Therefore, it takes 1.14 s to move the box 4.20 m.

I hope it helps you!

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