Si una bola rueda por el suelo describiendo una trayectoria en línea recta y tomamos medidas a cerca de su posición en diferentes instantes de tiempo.

DISTANCIA (m) 0 12 24 36

Tiempo (s) 4 25 46 67

a) ¿Cuál es su velocidad?

b) ¿Cuál es su distancia transcurridos 8 s?

c) ¿Cuál es su desplazamiento tras 8 s?

a) 0.57m/s

b) 4.56m

c) 4.56m

Explanation:

(a) To find the velocity you can calculate the average velocity for different intervals:

v1 = (12-0)m/(25-4)s=0.57m/s

v2 = (24-12)m/(46-25)s=0.57m/s

v3 = (36-24)m/(67-46)s=0.57m/s

the velocity is 0.57m/s

b) you use the expression:

x= vt = (0.57m/s)(8s)=4.56m

c) the displacement of the ball is the same as the previous question b)

4.56m

c)as speed changes, wavelength and frequency change.

everything changes!

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.