One of the hazards facing humans in space is space radiation: high energy charged particles emitted by the sun. During a solar flare the intensity of this radiation can reach lethal levels. One proposed method of protection for astronauts on the surface of the moon or Mars is an array of large electrically charged spheres placed high above areas where people live and work. The spheres would produce a strong electric field E to deflect the charge particles that make up space radiation. The spheres would be similar in construction to a Mylar balloon, with a thin electrically conducting layer on the outside surface on which a net + or-charge would be placed. A typical sphere might be 5m in diameter. Required:
To repel electrons in the radiation from a solar flare each sphere must produce an Electric field 1 x 10^6 N/C at 25 m from the center of the sphere. What net charge on sphere is needed?

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explanation:

a. are

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.