After world war ii the u. s. air force carried out experiments on the amount of acceleration a human can survive. these experiments, led by john stapp, were the first to use crash dummies as well as human subjects, especially stapp himself, who became an effective advocate for automobile safety belts. in one of the experiments, stapp rode a rocket sled that decelerated from 140 m/s (about 310 mi/h) to 70 m/s in just 0.6 s.

(a) what was the absolute value of the (negative) average acceleration?
m/s2

(b) the acceleration of a falling object if air resistance is negligible is 9.8 m/s/s, called "one g." what was the absolute value of the average acceleration in g's? (stapp eventually survived a test at 46 g's! )
g

11.9051g

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity = 9.8 m/s²

Absolute value of the (negative) average acceleration is 116.67 m/s²

The deceleration was 11.9051g

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.