A particle of mass m moves though a viscous medium. (See Figure
4.) In this medium, if the particle moves with a velocity
v, it experiences a drag force 
given by 
.
is known as the relaxation time. If a particle moves through
this medium without an external driving force, its velocity will decay
exponentially to zero with a characteristic time 
according to
. Essentially, the particle ``forgets'' what
it had been doing more that a few relaxation times in the past.
In this problem, the particle is illuminated from the left and absorbs
photons of wavelength 
at an average rate of I photons per unit
time. As a result, the particle
experiences an average force and is driven to the right at an average
velocity <v>. Because the photons arrive randomly as discrete
packets, the velocity of the particle is not steady and fluctuates
about the average with fluctuations of typical size 
. Your
task is to compute <v> and 
.
