The problem of finite-time output stabilisation of the double integrator is addressed applying the homogeneity approach. A homogeneous controller and a homogeneous observer are designed (for different degrees of homogeneity) ensuring the finite-time stabilisation. Their combination under mild conditions is shown to stay homogeneous and finite-time stable as well. Robustness and effects of discretisation on the closed-loop system obtained are analysed. The efficiency of the solution obtained is demonstrated in computer simulations.