The earth is 1.5 × 1011 m from the sun and takes a year to make one complete orbit. it rotates on its own axis once per day. it can be treated approximately as a uniform-density sphere of mass 6 × 1024 kg and radius 6.4 × 106 m (actually, its center has higher density than the rest of the planet, and the earth bulges out a bit at the equator). using this crude approximation, calculate the following.
a. what is vcm?
b. what is ktrans?
c. what is w, the angular speed of rotation around its own axis?
d. what is krot?
e. what is ktot?

. west

ok

explanation:

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.