Amarching band consists of rows of musicians walking in straight, even lines. when a marching band performs in an event, such as a parade, and must round a curve in the road, the musician on the outside of the curve must walk around the curve in the same amount of time as the musician on the inside of the curve. this motion can be approximated by a disk rotating at a constant rate about an axis perpendicular to its plane. in this case, the axis of rotation is at the inside of the curve. consider two musicians, alf and beth. beth is four times the distance from the inside of the curve as alf. knowing that: (a) if beth travels a distance s during time δt, how far does alf travel during the same amount of time= (1/4)s? (b) if alf moves with speed v, what is beth's speed? speed, in this case, means the magnitude of the linear velocity, not the magnitude of the angular velocity. a) 4v b) v c) v/4

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.

there are no atoms