An electron accelerated by a potential difference of 100V gains kinetic energy proportional to the voltage applied. When the voltage is increased to four times, the kinetic energy becomes four times greater, but the final speed does not increase by the same factor. Instead, the relationship between kinetic energy and speed shows that the final speed is actually doubled. This is derived from the equations relating energy and speed, confirming that the increase in voltage leads to a square root relationship in speed. Thus, doubling the speed occurs with a fourfold increase in voltage.
