Another group of students did an experiment to find out how the height at which a marble is dropped affects the size of impact crater formed. They filled a basin with flour and covered the surface with cocoa. They decided to change the marble size and the marble height each time. They measured the size of the craters. Conclusion: The marbles we dropped from higher heights made much bigger craters than the ones we dropped from lower heights. This is evidence that the farther the marbles falls, the bigger the crater is.

Is this a valid conclusion for these students to draw from the experiment they conducted? Why or why not?

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.

i would say