Its urgent pls help me :(

(4) The particle travels with a constant velocity until t0 and then comes to rest.

Explanation:

Uniform rectilinear motion is defined as the motion of a particle in a straight line with constant velocity, that is, there is no change in velocity over time.

And this can be determined by means of the following equation:

where:

x = final point [m]

xo = initial point [m]

v = velocity (slope) [m/s]

t = final time [s]

to = initial time [s]

So the slope in the graph gives the constant velocity

Therefore, after the time to there is no displacement, that is the particle comes to rest.

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.