Please help! Giving 20 points!! If two train cars, one of mass 1000 kg and the other of 1750 kg, are next to each other and connected by a compressed spring, and the spring releases so that the heavier car moves off at 4 m/s, what is the velocity of the other car?

Explanation:

Remark

This is a momentum question. Both cars are sitting still (v1 and v2 are both 0) to start with). When the spring is sprung), they both move but in opposite directions.

Let us say that v4 is minus.

Equation

0 = m3*v3 - m4* v4

Givens

m3 = 1750 kg

m4 = 1000 kg

v3 = 4 m/s

Solution

m3*4m/s - m4*x = 0

1750 * 4 - 1000*x = 0

1750 * 4 = 1000x

7000 = 1000 x

7000/1000 = x

x = 7 m/s

neither accurate nor precise.

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.