b
\({v_2}\,\, = \,\,20\,cm\,\, = \,\,0.2\,\,m/s,\,\,\,{v_1}\, = \,\,?\)

\(\Delta K\,\, = \,\, - q(\Delta \,V)\)

\(\frac{1}{2}\,mv_2^2\, - \,\,\frac{1}{2}\,mv_1^2\,\, = \,\, - \,\,q({V_B}\, - \,\,{V_A})\)

\(\frac{1}{2}\,\, \times \,\,{10^{ - 3}}[{(0.2)^2}\, - \,\,V_1^2]\,\, = \,\, - \,{10^{ - 8}}\,(0\,\, - \,\,600)\)

\({(0.2)^2}\,\, - \,\,v_1^2\, = \,\,12\,\, \times \,\,{10^{ - 3}}\,\,\, = \,\,\,4\,\, \times \,\,{10^{ - 2}}\, - \,\,v_1^2\,\, = \,\,1.2\,\, \times \,\,{10^{ - 2}}\)

\(v_1^2\, = \,\,2.8\,\, \times \,\,{10^{ - 2}}\,\,\,\therefore \,\,\,\,{v_1}\,\, = \,\,1.67\,\, \times \,\,{10^{ - 1}}\,\,m/s\)

\({v_1}\,\, = \,\,1.67\,\, \times \,\,{10^{ - 1}}\, \times \,\,{10^2}\,\, = \,\,16.7\,\,cm/s\)