The Kinetic-Molecular (K-M) Theory assumes a sample consisting of a large number of gas phase particles with an average kinetic energy that is proportional to the sample's absolute temperature. The particles are in continuous, random motion with an average kinetic energy that does not change as long as the temperature remains constant. No particles or energy are gained or lost by the sample.
Each particle in this sample is moving independently of all other particles and energy can be transferred between particles during collisions but all collisions are perfectly elastic. At any moment in time, some of the particles are moving very rapidly and some are moving very slowly. The fraction of the sample moving at any chosen velocity changes with temperature. It was long ago demonstrated that the actual distribution of particle energy (velocity) follows a Boltzmann Distribution. The nature of a Boltzmann Distribution is responsible for the differences in the peak positions and widths of the curves shown in the referenced graphs.
Additional information, discovered using an internet search engine, can be found at:
Kinetic Molecular Theory - and links therein
The Kinetic Molecular Theory
Kinetic Theory - and links therein
Physical Applications of Distribution Functions
Maxwell Speed Distribution
Try the links in the MadSci Library for more information on Chemistry.