A small ball is hung by a string from the ceiling of a train car, so that the ball hangs vertically.
Moving from rest, the train car accelerates forward, and continues to accelerate. A team of
scientists observes the behavior of the ball from various locations. From which scientist's frame
of reference does the motion of the ball appear to violate Newton's Law of Inertia?
O A. on the train station platform
OB. inside of the train car
o C. in a second train car moving with constant speed in the same direction as the
first train
OD. in a third train car moving with constant speed opposite the direction of the first
train

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.