Question

A smoke particle undergoing Brownian motion in air has a mass of 2.00 x 10 -5 kg.
a) what is the its average velocity if the temperature is 300 K?

b) what is its average kinetic energy?

The average kinetic energy of a particle or molecule of any mass is
Eav = (3/2) k T
where k is the Boltzmann constant,
1.38^10^-23 J/K, and
T is the temperature in Kelvin

Once you have the average KE, get the average (actually, r.m.s) velocity from
(1/2) M V^2 = Eav
M is the particle mass