An astronaut in his space suit and with a propulsion unit (empty of its gas propellant) strapped to his back has a mass of 146 kg. the astronaut begins a space walk at rest, with a completely filled propulsion unit. during the space walk, the unit ejects some gas with a velocity of 37 m/s. as a result, the astronaut recoils with a velocity of -0.39 m/s. after the gas is ejected, the mass of the astronaut (now wearing a partially empty propulsion unit) is 165 kg. what percentage of the gas propellant was ejected from the completely filled propulsion unit

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 ima (higher than 1m) will be greater than the ima with the height of 1m.