If a 1500 kg car is moving at 20 m/s and hits a brick wall and you know that it comes to rest in 0.80 s then how much force does the car sustain

consider the direction towards the wall as negative  and away from the wall as positive.

m = mass of the car colliding with the brick wall = 1500 kg

v₀ = initial velocity of the car towards the wall = - 20 m/s

v = final velocity of the car = 0 m/s

t = time taken by car to come to rest after collision = 0.80 s

F = force sustained by the car

using impulse-change in momentum

F t = m (v - v₀ )

inserting the values

F (0.80) = (1500) (0 - (- 20))

F (0.80) = 30,000

F = 30000/0.80

F = 37500 N

neither accurate nor precise.

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.