Two blocks of masses m and 3m are placed on a horizontal, frictionless surface. a light spring is attached to one of them, and the blocks are pushed together with the spring between them. a cord holding them together is burned, after which the block of mass 3m moves to the right with a speed of 2.4 m/s. what is the speed of the block of mass m?

The speed of the mass M is 7.2 meters per second

Explanation:

In this case because there aren't external forces on the system blocks-spring and the spring is light we should apply the conservation of linear momentum (P) that states:

(1)

Momentum is mass (m) times velocity (v) ( (2)) and Initial momentum is zero because the blocks are released form rest, so (1) is:

Using (2) on (1):

(3)

It's important to note that momentum and velocity are vector quantities so we should take care of directions, assuming right direction as positive, velocity of 3M mass is positive, and velocity of M mass is negative, (3) is:

solving for

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.