What did the summer and winter solstices indicate to ancient people?

The solstice of summer and winter indicated to the ancient people about the preparatory measures to be up taken for the longer nights (sun was going to come up for another half year) especially to come up.

Explanation:

From the summer solstice until the winter solstice, nights get lengthier in duration and ancient people feared that it may someday overtake the whole of 24 hours of time. In accordance with that belief, they prepare for the hardship of winter to be faced and prayed to God against the fearful belief.

With the winter solstice coming over, they thanked God for the relief against their ghastly belief which has later turned up to be celebrated as the Christmas and birth of the deity.

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.