Sam is riding his bike in the park when he sees a soccer ball rolling toward him. he applies his brakes to slow down. once he stops, he notices that the tires on his bike became warmer after he applied the brakes. why did the tires on sam's bike become warmer as he applies the brakes on his bike?

When Sam presses the brake lever, a pair of rubber shoes  clamps onto the metal inner rim of the front and back wheels. As the brake shoes rub  against the wheels, friction is caused and  the kinetic energy possessed by the vehicle is converted into heat which slows down the vehicle.

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.