At the instant a traffic light turns green, a car starts with a constant acceleration of 1.3 m/s2. at the same instant a truck, traveling with a constant speed of 7.0 m/s, overtakes and passes the car.
(a)how far beyond the traffic signal will the car overtake the truck?
(b)what will the velocity of the car be at that instant?

(a) Distance traveled = 75.3846 m

(b) Velocity of car at that instant will be 14 m/sec

Explanation:

We have given acceleration of the car

Initial velocity of the cart u = 0 m/sec

(a) According to second equation of motion we know that

So distance traveled by car

As the truck is moving with constant speed

So distance traveled by truck

As the truck overtakes the car

So

So distance traveled

(b) From second equation of motion we know that v = u+at

So v = 0+1.3×10.769 = 14 m /sec

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.