Show, with the aid of a sketch, how the electric potential varies in the space cl positive point charge, and ii) close to a negative point charge. ose to i) a sketch also how the electric potential energy of both a positive charge and a negative charge varies as a function of distance from i) a positive point charge and i) a negative point charge. how how the electric potential close to a point charge can be obtained from coulomb's law (b) to recharge a 12-v battery, a battery charger must move 3.6 x 10% c of charge from the negative to the positive terminal. what amount of work is done by the battery charger? how many kilowatt hours is this? (c) how much electrical charge is needed to raise an isolated metal sphere of radius 1.0 m to a potential of 1 .0 106 v? (d) what is the resistance of 1,000 m of 4-mm diameter copper wire? (the resistivity of copper, pou 1.7 x 10-8 ω m)

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.