Aguitar string produces 4 beats/second when sounded with
a250hz tuning fork and 9 beats/second when sounded with a 255
hztuning fork. what is the vibrational frequency?

In first case vibrational frequency will be 246 Hz and 254 Hz

In second case vibrational frequency will be 264 Hz and 246 Hz

Explanation:

We have given a guitar produces 4 beats per second when sounded with 250 Hz and produce 9 beats per second when sounded with 255 Hz

Expression of beat frequency is

Here is vibrational frequency

So

For second case

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement

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.