Aspacecraft is in empty space. it carries on board a gyroscope with a moment of inertia of ig = 18.5 kg m2 about the axis of the gyroscope. the moment of inertia of the spacecraft around the same axis is is = 5.00 105 kg m2. neither the spacecraft nor the gyroscope is originally rotating. the gyroscope can be powered up in a negligible period of time to an angular speed of 145 rad/s. if the orientation of the spacecraft is to be changed by 28.0, for what time interval should the gyroscope be operated?

a) are muscles that have bands.

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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.