Solar coronal mass ejections (CMEs) show a large variety in their kinematic properties. CMEs originating in active regions and accompanied by strong flares are usually faster and accelerated more impulsively than CMEs associated with filament eruptions outside active regions and weak flares. It has been proposed more than two decades ago that there are two separate types of CMEs, fast (impulsive) CMEs and slow (gradual) CMEs. However, this concept may not be valid, since the large data sets acquired in recent years do not show two distinct peaks in the CME velocity distribution and reveal that both fast and slow CMEs can be accompanied by both weak and strong flares. We present numerical simulations which confirm our earlier analytical result that a flux-rope CME model permits describing fast and slow CMEs in a unified manner. We consider a force-free coronal magnetic flux rope embedded in the potential field of model bipolar and quadrupolar active regions. The eruption is driven by the torus instability which occurs if the field overlying the flux rope decreases sufficiently rapidly with height. The acceleration profile depends on the steepness of this field decrease, corresponding to fast CMEs for rapid decrease, as is typical of active regions, and to slow CMEs for gentle decrease, as is typical of the quiet Sun. Complex (quadrupolar) active regions lead to the fastest CMEs. ; Comment: 4 pages, 3 figures, published in Astron. Nachr. 328, 743 (2007). Minor update to conform to published paper, with minor language improvements and citation updates included