Alice and tom dive from an overhang into the lake below. tom simply drops straight down from the edge, but alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. neither person experiences any significant air resistance. compare the time it takes each of them to reach the lake below. alice and tom dive from an overhang into the lake below. tom simply drops straight down from the edge, but alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. neither person experiences any significant air resistance. compare the time it takes each of them to reach the lake below. tom reaches the surface of the lake first. alice reaches the surface of the lake first. alice and tom will reach the surface of the lake at the same time.

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.