Two particles move along the 
-axis uniformly with speeds 
and 
. At the initial moment the first point was 
to the left of the origin and the second 
to the right of the origin. When will the first point catch up with the second? Where will this take place? Plot the graph of the motion.
Extracted from A. A. Pinsky. (1980). Problems in Physics.
Set-up.
Rename the two particles by 
and 
. The velocity of particle is 
and that of particle is 
. The particles at time 
are located on the -axis with -coordinates 
and 
respectively.
Roughwork.
When :
when 
:
when 
:
when 
:
when 
:
when 
:
when 
:
when 
:
Solution.
The positions 
, 
of particle , can be expressed in a function of discrete time interval
,
i.e.,
or simply, in continuous time intervals,
Particle will meet particle when 
at some time 
, as
so the place of meeting is
.