Acrylic paint can be used on plastic, but it is not specifically designed for this use. Acrylics don't always hold up as well to repeated handling as other paints, and they work better on surfaces that allow air through, like wood and paper, than they do on plastic. However, if combined with the proper sealers and base coats, acrylics can be adapted to almost any surface.
Adapting Acrylics to Plastic Surfaces
Since acrylics are not made specifically for use on plastics, you will have to work with them a little bit if you really need that acrylic look. To prevent your acrylic paint from pealing off later, you will need first to apply a base coat. Your base coat should be a paint that is more well adapted for use with plastic or metal, such as oil paint or enamel. Once you have applied a base coat, you are safe to apply acrylic paint over it.
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Adapting Acrylics to Handling
Acrylics aren't especially good for painting objects that will be handled repeatedly. If your plastic object is a toy model that you plan to take down from the shelf and get dozens of fingerprints on, you should put a sealer coat over your acrylic paint. On the other hand, if you are painting a decorative panel for an out-of-reach spot on your wall, handling won't be a problem and you can let the bare acrylic show through.
If you need to use a sealer there are plenty of spray-on kinds such as Krylon that are available in different types of finishes, so you can choose whether to use a matte finish or a glossy finish. This not only will protector your work from being damaged by handling, it also will protect the acrylic paint from being smudged with water. And of course, using a finish will give your work that finished look.
If all of this seems a little too much trouble for what you're trying to do, consider oil or enamel paint. These paints work well with plastics and don't require base coats or sealers, so they will save you time in the long run, even though they won't dry as quickly as acrylic paint.