Electrons in an electric circuit pass through a resistor. the
wire on either side of the resistor has the same diameter. (a) how
does the drift speed of the electrons before entering the resistor
compare to the speed after leaving the resistor? explain your reasoning.
(b) how does the potential energy for an electron before
entering the resistor compare to the potential energy after leaving
the resistor? explain your reasoning.

On the off chance that u know the condition I = NEVA where N= no. thickness of electrons, E= charge on a solitary electron, V=drift speed ,and A=area of cross-segment. 
since the widths are same , the zone of cross-segment must be same and thusly the float speed likewise will be the same 
b) as u know current streams from higher to bring down potential.The electrons will spill out of lower potential to higher potential. Higher potential suggests higher potential vitality and accordingly potential vitality must increment.