An electron and a proton are held on an \(x\) axis, with the electron at \(x=+1.000 \mathrm{~m}\) and the proton at \(x=\) \(-1.000 \mathrm{~m}\).

(a) How much work is required to bring an additional electron from infinity to the origin? 

\((b)\) If, instead of the second electron coming in from infinity, it is initially at \(x=+20.00 \mathrm{~m}\) on the axis and is given an initial velocity of \(500.0 \mathrm{~m} / \mathrm{s}\) toward the origin, does it reach the origin? If so, what is its speed at the instant it reaches the origin? If not, how close to the origin does it come?