Two cars, one of mass 1300 kg, and the second of mass 2400 kg, are moving at right angles to each other when they collide and stick together. the initial velocity of the first car is 12 m/s in the positive x direction and that of the second car is 18 m/s in the positive y direction.
what is the magnitude of the velocity of the wreckage of the two cars immediately after the collision?

To solve this problem we will apply the momentum conservation theorem, that is, the initial momentum of the bodies must be the same final momentum of the bodies. The value that will be obtained will be a vector value of the final speed of which the magnitude will be found later. Our values are given as,

Using conservation of momentum,

Solving for

Using the properties of vectors to find the magnitude we have,

Therefore the magnitude of the velocity of the wreckage of the two cars immediately after the collision is 12.4135m/s

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.