We measure the vertical velocities of elevators, pedestrians climbing stairs, and drones (flying unmanned aerial vehicles), by means of smartphone pressure sensors. The barometric pressure obtained with the smartphone is related to the altitude of the device via the hydrostatic approximation. From the altitude values, vertical velocities are derived. The approximation considered is valid in the first hundred meters of the inner layers of the atmosphere. In addition to pressure, acceleration values were also recorded using the built-in accelerometer. Numerical integration was performed, obtaining both vertical velocity and altitude. We show that data obtained using the pressure sensor is significantly less noisy than that obtained using the accelerometer. Error accumulation is also evident in the numerical integration of the acceleration values. In the proposed experiments, the pressure sensor also outperforms GPS, because this sensor does not receive satellite signals indoors and, in general, the operating frequency is considerably lower than that of the pressure sensor. In the cases in which it is possible, comparison with reference values taken from the architectural plans of buildings validates the results obtained using the pressure sensor. This proposal is ideally performed as an external or outreach activity with students to gain insight about fundamental questions in mechanics, fluids, and thermodynamics.