We deploy the immersogeometric approach for tracking moving objects. The method immerses objects into non-boundary-fitted meshes and weakly enforces Dirichlet boundary conditions on the object boundaries. The object motion is driven by the integrated surface force and external body forces. A residual-based variational multiscale method is employed to stabilize the finite element formulation for incompressible flows. Adaptively refined quadrature rules are used to better capture the geometry of the immersed boundaries by accurately integrating the intersected background elements. Treatment for the freshly-cleared nodes (i.e. background mesh nodes that are inside the object at one time step, but are in the fluid domain at the next time step) is considered. We assess the accuracy of the method by analyzing object motion in different flow structures including objects freely dropping in viscous fluids and particle focusing in unobstructed and obstructed micro-channels. We show that key quantities of interest are in very good agreements with analytical, numerical and experimental solutions. We also show a much better computational efficiency of this framework than current commercial codes using adaptive boundary-fitted approaches. We anticipate deploying this framework for applications of particle inertial migration in microfluidic channels.