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!

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day