Consider a cart pushed along a track with a certain force, if the force remains the same while the mass of the cart decreases to half, the acceleration of the cart .

Doubles (under the assumption there is no friction between the cart and the track)

Explanation:

The acceleration produced by a force, F, on a mass, m, is given by

It is seen that, when the force is constant, the acceleration is inversely proportional to the mass.

Thus, if the mass is halved,

The acceleration is doubled.

However, if there's friction between the track and the cart, the reduction of the mass reduces friction between. While the applied force remains constant, the effective force increases. The acceleration will then depend additionally on the values of the coefficients of friction and the applied force.

which piece of furniture will have the most inertia and give the furniture movers the most difficulty in moving?  

answer

a 75kg dining table

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.