The fluid movement of an arm is controlled by multiple parameters that can be set independently. Recent studies argue 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 independently-specifiable dynamics. Using a task where monkeys made sequential, varied arm movements, we show that independent parameters of arm movements are independently encoded in the low-dimensional trajectories of population activity: each movement’s direction by a fixed neural trajectory and its urgency by how quickly that trajectory was traversed. Network models show this latent coding allows the direction and urgency of arm movement to be independently controlled. 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 the initial conditions of those dynamics.