Due to threats to human safety, remotely controlled manipulators are more and more often used to carry out rescue tasks in hazardous zones. To ensure high efficiency and productivity of their work, intuitive control systems are necessary, e.g., master-slave and drive systems that maximize the speed of working movements by copying the movements of the operator’s hands and are adapted to human perception and capabilities. Proper design of manipulator drive and control systems, therefore, requires knowledge of the acceleration and velocity of hand movements as signals controlling manipulators. This paper presents the results of tests of speed and acceleration in the implementation of the hand when making precise movements and moving objects over short distances (0.4–0.5 m) and during relatively long-distance reaching movements (0.73–0.93 m). Research has shown that, at short distances, the hand movements do not reach the maximum speed, while at longer distances, there is a period of constant maximal speed. In addition, studies have shown that the maximum speed of manipulation movements (longitudinal, lateral, and vertical) does not depend on the direction of movement. Moreover, precise movements were performed at a much slower velocity than reaching movements.