We reduce a one-dimensional model of an active segment (AS), which is used, for instance, in the description of contraction driven cell motility on tracks, to a zero-dimensional model of an active particle (AP) characterized by two internal degrees of freedom: position and polarity. Both models give rise to hysteretic force-velocity relations showing that an active agent can support two opposite polarities under the same external force and that it can maintain the same polarity while being dragged by external forces with opposite orientations. This double bi-stability results in a rich dynamic repertoire which we illustrate by studying static, stalled, motile and periodically repolarizing regimes displayed by an active agent confined in a visco-elastic environment. We show that the AS and AP models can be calibrated to generate quantitatively similar dynamic responses.