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Through what potential would one need to accelerate an electron in order to achive a velocity of 60% of that of light.,starting from rest.

The final speed of the electron is v_f = 0.6(3.00×10⁸ m/s) = 1.80×10⁸ m/s.

At this speed, the energy (non-relativistic) is the kinetic energy,

E = ½mv_f² = 0.5(9.11×10^-31 kg)(1.80×10⁸ m/s)² = 1.48×10^-14 J.

This energy must equal the change in potential energy from moving through a potential difference, V, E = DPE = qV.

Therefore:
V = E/q = (1.48×10^-14 J)/(-1.6×10^-19 C) = -9.25×10⁴ V.