Does the velocity of the electron change or remain constant between the anode and the screen?
Back to Newton’s Laws! The bit about “Every body continues in its state of rest or uniform motion in a straight line unless it is acted upon by an externally impressed force”. The (negatively charged) electron is subject to a force due to the electric field between cathode and anode which causes it to accelerate while it’s within that field. When it leaves that field, there is no force to cause further acceleration and the electron continues at constant velocity. There is a complication to the story… Velocity is a vector quantity – it has both magnitude and direction. What you do find in the area between anode and screen are the x and y deflection plates (or external magnetic deflection coils) that move the spot about the display screen. If they are active, they are changing the direction of the electron beam and therefore changing the velocity of the electrons.