We describe a series of molecular dynamics simulations performed on model cation-water systems at 25 degrees C representing the behavior of Li+, Na+, K+, Rb+, and Cs+ in an electric field of 1.0 V/nm and in its absence. The TIP4P model was used for water and TIPS potentials were adapted for the ion-water interactions. The structure of the surrounding water molecules around the cations was found to be independent of the applied electric field. Some of the dynamic properties, such as the velocity and force autocorrelation functions of the cations, are also field independent. However, the mean-square displacements of the cations, their average drift velocities, and the distances traveled by them are field dependent. The mobilities of the cations calculated directly from the drift velocity or the distance traveled by the ion are in good agreement with each other and they are in satisfactory agreement with each other and they are in satisfactory agreement with the mobilities determined form the mean-square displacement and the velocity autocorrelation function in the absence of the field. They also show the same trends with ionic radii that are observed experimentally; the magnitudes are however, smaller than the experimental values in real water by almost a factor of 2. It is found that the water molecules in the first solvation shell around the small Li+ ion are stuck to the ion and move with it as an entity for about 190 ps, while the water molecules around the Na+ ion remain for 35 ps, and those around the large cations stay for 8-11 ps before significant exchange with the surroundings occurs. The picture emerging from this analysis is that of a solvated cation whose mobility is determined by its size as well as the static and dynamic properties of its solvation sheath and the surrounding water. The classical solventberg model describes the mobility of Li+ ions in water adequately but not those of the other ions.