Answer:
It takes 1.14 s to move the box 4.20 m.
Explanation:
Using Newton's second law we have:
[tex]Fcos(35)-F_{f}=ma[/tex]
[tex]Fcos(35)-\mu mg=ma[/tex]
F is the force exerted and m the mass of the books
[tex]Fcos(35)-\mu mg=ma[/tex]
[tex]477cos(35)-(0.58*315)=\frac{315}{9.81}a[/tex]
So, the books accelerate at:
[tex]a=6.48\: m/s^{2}[/tex]
We know that the initial velocity is zero, so using the kinematic position equation, we have:
[tex]x=\frac{1}{2}at^{2}[/tex]
So, we just need to solve the equation for t.
[tex]4.2=\frac{1}{2}6.48t^{2}[/tex]
[tex]t=\sqrt{\frac{2*4.2}{6.48}}[/tex]
Taking the positive value of t:
[tex]t=1.14\: s[/tex]
Therefore, it takes 1.14 s to move the box 4.20 m.
I hope it helps you!
