You want to move a 4- kg bookcase to a different place in the living room. if u push with a force of 65 n and the bookcase accelerates at 0.12 m/s2 what is the coefficient of kinetic friction between the bookcase and the carpet

1.65

Explanation:

The equation of the forces along the horizontal direction is:

(1)

where

F = 65 N is the force applied with the push

is the frictional force

m = 4 kg is the mass

is the acceleration

The force of friction can be written as (2), where

is the coefficient of kinetic friction

R is the normal force exerted by the floor

The equation of forces along the vertical direction is

(3)

since the bookcase is in equilibrium. Substituting (2) and (3) into (1), we find

And solving for ,

whichever one it is, it's definitely not one that you included on the list you provided.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.