The electron travels through a potential difference of [tex]\Delta V =2500 V[/tex]. This means that the loss of electrostatic potential energy of the electron is
[tex]\Delta U = q \Delta V= (-1.6 \cdot 10^{-19}C)(2500 V)=-4 \cdot 10^{-16}J[/tex]
where q is the electron charge.
For the law of conservation of energy, the electron (starting from rest and accelerated by the potential difference) acquired a kinetic energy equal to the negative of this loss of potential energy:
[tex]\Delta K=-\Delta U[/tex]
where [tex]\Delta K =K_f - K_i = K_f[/tex] because the electron is initially at rest and so its kinetic energy is zero. Since
[tex]K_f= \frac{1}{2}mv^2 [/tex]
where m is the electron mass, we can find the final velocity v of the electron:
[tex]v= \sqrt{ \frac{2K_f}{m} }= \sqrt{ \frac{2\cdot 4 \cdot 10^{-16} J}{9.1 \cdot 10^{-31} kg} }=3.0 \cdot 10^7 m/s [/tex]
