(a) a light-rail commuter train accelerates at a rate of 1.35 m/s2 . how long does it take to reach its top speed of 80.0 km/h, starting from rest?
(b) the same train ordinarily decelerates at a rate of 1.65 m/s2 . how long does it take to come to a stop from its top speed?
(c) in emergencies the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. what is its emergency deceleration in m/s2 ?

(a) Time t = 16.46 sec

(b) Time t =13.466 sec

(c) Deceleration =

Explanation:

(a) As the train starts from rest its initial velocity u = 0 m/sec

Acceleration

Final speed v = 80 km/hr

From first equation of motion v =u+at

So

(b) Now initial speed u = 22.22 m/sec

As finally train comes to rest so final speed v=0 m/sec

Deceleration

So

(c) We have given that initial velocity = 80 km/hr = 22.22 m/sec

Final velocity v = 0 m/sec

Time t = 8.30 sec

So acceleration is given by

As acceleration is negative so it is a deceleration

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.