  This paper is devoted to study the controllability of a one-dimensional
fluid-particle interaction model where the fluid follows the viscous Burgers
equation and the point mass obeys Newton's second law. We prove the null
controllability for the velocity of the fluid and the particle and an
approximate controllability for the position of the particle with a control
variable acting only on the particle. One of the novelties of our work is the
fact that we achieve this controllability result in a uniform time for all
initial data and without any smallness assumptions on the initial data.
