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Direct detection experiments tend to lose sensitivity in searches for sub-MeV light dark matter candidates due to the threshold of recoil energy.However,such light dark matter particles could be accelerated by energetic cosmic rays,such that they could be detected with existing detectors.We derive constraints on the scattering of a boosted light dark matter particle and electron from the XENON100/1T experiment.We illustrate that the energy dependence of the cross section plays a crucial role in improving both the detection sensitivity and also the complementarity of direct detection and other experiments.