Speed of Electron in Two-Charge System

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In a two-charge system with charges of +3.00*10^-9 C and +2.00*10^-9 C separated by 50.0 cm, an electron is released from rest at the midpoint. To find the electron's speed when it is 10.0 cm from the +3.00*10^-9 C charge, the potential energy must be calculated with respect to each charge, not between the charges. The correct formula for initial potential energy is U_i = k q_1 q_e/r_1 + k q_2 q_e/r_2, where r_1 and r_2 are the distances from the electron to each charge. The difference in potential energy (U_i - U_f) can then be equated to kinetic energy to find the speed. Accurate calculations of distances and potential energy are crucial for determining the correct speed of the electron.
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Two stationary point charges and +3.00*10^-9 C and +2.00*10^-9 C
are separated by a distance of 50.0 cm. An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges. What is the speed of the electron when it is 10.0 cm from the +3.00 *10^-9 C charge? I first tried to find U_i and U_f by using the formula U_i= (k*e*q_1*q_2)/(r_1) and then the same for U_2=(k*e*q_1*q_2)/(r_2) I used .25 for r_1 and .35 for r_2. After that I and used the formula U_i - U-f = 1/2*1/e*m*v^2. It didn't work, maybe I am using the wrong values for the radii. Please Help!
 
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You need to calculate the potential energy of the electron with respect to each charge, not the potential energy of the charges with respect to each other. Like this:
U_i = k q_1 q_e/r_1 + k q_2 q_e/r_2
 

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