In a parabolic band, the momentum and velocity relaxation rates of electrons (associated with scattering) are identical. However, if a magnetic field is present, they are fundamentally different quantities that can have opposite signs over quite wide ranges of the electron's kinetic energy. Consequently, it is possible that electrons will lose momentum during a scattering event and yet gain velocity. In narrow InAs quantum wires subjected to a high magnetic field, we show that this can cause the ensemble average momentum and velocity relaxation rates to have opposite signs in realistic situations.