Speed distribution for a sample of N gas particles

[esoteric deviance]

Homework Statement

http://www.fileden.com/files/2006/11/15/381656/19.39.png

The figure shows a hypothetical speed distribution for a sample of N gas particles (note that P(v) = 0 for speed v > 2v₀).

(b) What is the value of v_avg/v₀?

Homework Equations

v_avg = int[vP(v)]dv

The Attempt at a Solution

The solutions manual says that, for the triangular portion of the distribution, P(v) = av/v₀.
This may be a stupid question, but how does one get that?

(only need help with that portion of the problem for now)

 

[Dick]

Well, for the given function P(v), P(0)=0, P(v0)=a, and the function is linear in v. So it looks like your graph.