Aspherical protein of molar mass 4.5x100 g/mol and density 1.33x10 kg/m3 is placed at the top of a 2-cm-long centrifuge tube filled with a fluid of density 1.1x103 kg/m3 and viscosity of 1.8x10 pa-s. in the centrifuge, the sample is placed at a distance 20 cm from the rotation axis, and the centrifuge is then run at 3000 revolutions per second (i. e. 3000 hz). a) what is the diameter of these proteins? b) what is the terminal speed of these proteins under centrifugation? c) approximately how long will it take the proteins to sediment to the bottom of the tube?

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.

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm