# Maxwell velocity distribution

Dear
I have problem with determine the minimum speed in this problem , I think the the maximum speed equal to the average speed and the most probable speed can be obtain by derive equation and equally to zero .Is my solution correct?

The speed distribution function for N particles in a fixed volume is given by f (V) = AV(B - V)/B^3,
where V (>0) is the particle speed, and A and B are positive constants. Determine:
(a) The minimum speed Vmin and maximum speed Vmax.
b) The most probable speed where the probability density function is the largest.

mfb
Mentor
I think the the maximum speed equal to the average speed
If that would be true, all particles would have to have the same speed.

I have problem with determine the minimum speed in this problem
What is the minimal V where f(V) is not zero?
If you don't see that, make a sketch of f(V).

and the most probable speed can be obtain by derive equation and equally to zero
Right.

If that would be true, all particles would have to have the same speed.

What is the minimal V where f(V) is not zero?
If you don't see that, make a sketch of f(V).

Right.

the minimum when B=v=0 and what about the maximum

mfb
Mentor
the minimum when B=v=0
Why B=?
A and B are parameters, you cannot set their values.

Did you draw the sketch I proposed? Do you see the maximum?

Andrew Mason
Homework Helper
Dear
I have problem with determine the minimum speed in this problem , I think the the maximum speed equal to the average speed and the most probable speed can be obtain by derive equation and equally to zero .Is my solution correct?

The speed distribution function for N particles in a fixed volume is given by f (V) = AV(B - V)/B^3,
where V (>0) is the particle speed, and A and B are positive constants. Determine:
(a) The minimum speed Vmin and maximum speed Vmax.
b) The most probable speed where the probability density function is the largest.
First of all, this is not a Maxwellian distribution. The distribution is determined by this equation.

The minimum speed is the speed for which the distribution f(V) < 1. Since we don't know the values of A and B you cannot really determine that so assume it is very close to f(V) = 0.

How is the maximum related to the rate of change of f(V) with respect to V?

AM