Lipid membranes form the barrier between the inside and outside of cells and many of their subcompartments. As such, they bind to a wide variety of nano- and micrometer sized objects and, in the presence of strong adhesive forces, strongly deform and envelop particles. This wrapping plays a key role in many healthy and disease-related processes. So far, little work has focused on the dynamics of the wrapping process. Here, using a model system of micron-sized colloidal particles and giant unilamellar lipid vesicles with tunable adhesive forces, we measure the velocity of the particle during its wrapping process as well as the forces exerted on it by the lipid membrane. Dissipation at the contact line appears to be the main factor determining the wrapping velocity and time to wrap an object.