A box with volume V confines 18 particles with identical mass m and the following speeds: three particles with speed v, one particle with speed 2v, four particles with speed 3v, three particles with speed 4v, five particles with speed 5v, and two particles with speed 6v. (Use the following as necessary: v.)

(a). What is the most probable speed of the particles in this box?

vmp =

(b). What is the average speed of the particles in this box?

vav =

(c). What is the rms speed of the particles in this box?

vrms =