Acar traveling at 105 km/h strikes a tree. the front end of the car compresses and the driver comes to rest after traveling 0.80 m. (a) what was the magnitude of the average acceleration of the driver during the collision? (b) express the answer in terms of “g’s,” where 1.00 g = 9.80 m/s^2.

Part a)

a = 531.7 m/s/s

Part b)

a = 54.25 g

Explanation:

Part a)

Initial speed of the car is given as

now we have

now we know that it stops in 0.80 m

now by kinematics we have

so we will have

Part b)

in terms of g this is equal to

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.