Past exam of the physics 1 paper of the University of Oxford / 2013 resit / 6

The external work equals the change in relativistic kinetic energy, $W=m_e{c}^2({\gamma }_f-{\gamma }_i)$. With $m_e{c}^2=511\mathrm{keV}$,The rest energy cancels between endpoints. At these speeds, the nonrelativistic estimate $\frac{1}{2}{m}_e{c}^2(0.11^2-0.10^2)=0.53655\mathrm{keV}$ is close but slightly smaller.

Applying the same work-energy theorem at the higher pair of speeds givesThe identical increment $0.01c$ now needs about two thousand times as much work. The growth follows from the rapidly increasing Lorentz factor near the speed of light.