A fisherman has caught a very large, 5.0 kg fish from a dock that is 2.0 m above the water. He is using lightweight fishing line that will break under a tension of 60 N or more. He is eager to get the fish to the dock in the shortest possible time.

If the fish is at rest at the water's surface, what is the least amount of time in which the fisherman can raise the fish to the dock without losing it?

To solve this problem we will start by applying the equilibrium equations, for which the net force applied on the body is given by the difference between the weight of the object and the tension applied on the fishing line. Starting from finding the force, we can proceed to find the maximum resistant acceleration of the object and finally applying the linear kinematic equations for the duration of the process. Now calculating the Force we have,

By Newton's second law we have finally that,

Here m is the mass and a the acceleration,

The time by the fish can be calculated through the kinematic linear equation, then

There is not initial velocity because the fish initially is at rest,

Rearranging to find the time,

Therefore the amount of time in which the fisherman can raise the fish to the dock without losing it is 1.35s

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.