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What is The speed with which the electrons travel from the
filament of cathode to the anode depends upon and explain in detail?
The primary functions of the power supply of an X-ray machine are to:

Provide a low-voltage current to heat the X-ray tube filament.
Generate a high potential difference to accelerate electrons from the cathode to the focal spot on the anode. The X-ray tube and two transformers lie within an electrically grounded metal housing called the head of the X-ray machine.

White and Pharoah, pg-6