Hemodynamic management of sepsis in the emergency department relies on fluid resuscitation and vasoactive therapy to maintain adequate blood pressure and end-organ perfusion. While typical practice targets certain thresholds of blood pressure (such as 65 mmHg mean arterial or 90 mmHg systolic blood pressure [SBP]), little consideration is given to temporal dynamics of blood pressure. In this work, we use unsupervised learning methods to reveal characteristic SBP trajectories in the two hours either surrounding the start of hypotensive episodes (SBP <; 90 mmHg) or immediately preceding the initiation of vasopressor therapy. Our results show that hypotensive episodes tended to either resolve very quickly (within 40 minutes) or extend for prolonged periods (at least 1 hour). Those with prolonged hypotension constituted 74% of all patients with at least one measurement of SBP <; 90 mmHg. Of them, patients who entered hypotension by a large, acute drop from a normal SBP over the preceding hour had a greater incidence of subsequent vasopressor administration than those with a more gradual decline into hypotension. Overall, our results suggest that a significant subset of patients, especially those with stable but low SBP, should have received vasopressors when they did not, or should have received them sooner. Dynamic trajectories appear to be important factors in clinical practice of hemodynamic management of sepsis.