The steel compression ring for the piston of an automobile engine has a mass of 40 g. the ring is irradiated with neutrons until it has an activity of 2.5 ci of (t = 44.529 d) distributed uniformly throughout. the ring is installed in an engine and removed 30 days later. if the 22 l of crankcase oil has an average activity due to of 0.023 d/s per cubic centimeter, what mass (g) of steel was worn off the piston ring?

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.

god i hope this !