For this part, imagine that the string is wound around the center axle of a yo-yo; the axle radius is raxle, but the yo-yo casing has a radius rcasing≫raxle and moment of inertia i≫mr2axle. in the limit the moment of inertia of the yo-yo i→∞ and the mass m of the yo-yo remains finite, what magnitudes would you expect for the tension t in the vertical section of string and the downward acceleration a of the center of mass? choose the option that best describes the limiting values of t and a under the conditions given.

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.

answer: 31, 5556. 952 seconds