What are the period and (constant) speed of a person on a carousel if the person has an acceleration magnitude of 0.80 m/s2 (direction is toward the center) when she is standing 4.0 m from the axis? (b) what are her acceleration magnitude, and speed if she then moves in to a distance of 2.0 m from the carousel center and the carousel keeps rotating with the same period?

part a)

Centripetal acceleration is given as

Now time period is given as

constant speed is given as

part b)

now when she is at radius r = 2 m

centripetal acceleration is given as

now the linear speed is given as

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.

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2