The fluid movement of an arm requires multiple spatiotemporal parameters to be set independently. Recent studies have argued that arm movements are generated by the collective dynamics of neurons in motor cortex. An untested prediction of this hypothesis is that independent parameters of movement must map to independent components of the neural dynamics. Using a task where three male monkeys made a sequence of reaching movements to randomly placed targets, we show that the spatial and temporal parameters of arm movements are independently encoded in the low-dimensional trajectories of population activity in motor cortex: Each movement's direction corresponds to a fixed neural trajectory through neural state space and its speed to how quickly that trajectory is traversed. Recurrent neural network models show this coding allows independent control over the spatial and temporal parameters of movement by separate network parameters. Our results support a key prediction of the dynamical systems view of motor cortex, but also argue that not all parameters of movement are defined by different trajectories of population activitySignificance Statement From delicate strokes while drawing to ballistic swings while playing tennis, a skilled arm movement requires precise control of both its direction and speed. Motor cortex is thought to play a key role in controlling both, but it is unclear how they are jointly controlled. We show here that the population activity in motor cortex represents both the spatial and temporal properties of arm movements in the same low-dimensional signal. This representation was remarkably simple: the movement's direction is represented by the trajectory that signal takes; the movement's speed by how quickly the signal moves along its trajectory. Our network modelling shows this encoding allows an arm movement's direction and speed to be simultaneously and independently controlled.