We are given that n(E) dE = A(E^0.5) dE gives us the no. of particles between E and E+dE, where E is the energy of a particle and A is a constant. We are told to model the particles as classical particles i.e E=0.5m(v^2) We need to find the speed distribution. This is of the form N(v)dV, where N is a function of v. We were given a solution that says substitute dE = mv dv into our first eq'n and we get A (E^0.5) mv dv = A ((m^3)/2)^0.5) (v^2)dv. Therefore we conclude that N(v)dv = A ((m^3)/2)^0.5) (v^2)dv. This means that we initially have to assume that n(E)dE = N(v)dv , and I am not sure about the logic of this. There must be some physical principle about why the distribution of particles with respect to one variable can be transformed into another. Thanks v. much.