11. A book with many printing errors
contains the following four different
equations for the displacement y
of a particle undergoing a certain
was di
periodic motion:
(a) y = sin
2100
T
(b) y = sin (vt).
A
(c) y = --sin
7
0
and
A
(a) y = (1052)s cos
21
T
where A is maximum displacement
of the particle, v is speed of the
particle, t is the time and T is the
periodic time. Find out the wrong
equations on dimensional grounds
t
2 Precio

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.

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm