A vehicle is moving at a speed of 20m/s suddenly the driver sees a fallen tree on the road, he instantly applies the brakes that subject the car to a deceleration of -2m/s².Find a) Time required by the car to stop.
b) distance covered before stopping.

b) Distance covered before stopping.

Explanation:

If you want to find the distance d required to come to a stop starting at some initial speed v, with braking acceleration a, use the kinematic relation  

vf2 - vi2 = 2ad

vi = initial speed at the moment braking begins = v

vf = final speed = 0 (comes to a full stop)

-v2 = 2ad

d = -v2/(2a)

a electromagnetic waves

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.