Solve the following problem given below:
Problem: Particle track detectors are used to measure the speed of particles if the lifetime of the particle is known. Particle X has a lifetime of 256.2 ps. These particles are created in an experiment inside the detector by a given reaction. The particles leave 14.0 cm long tracks on average before they decay into other particles not observable by the detector.
Part A: What is the average speed of the particles in terms of the speed of light?
Please explain each step and equations used to get the solution.