Don't rush out to buy a new bathtub because of a minor blemish. Replacement costs are fairly high, but repair costs are not. Acrylic bathtubs have a solid surface, not a sprayed or painted on finish, which makes repairs rather easy to complete.
Very fine surface scratches or dulling
On minor surface scratches or dull spots, use liquid polish or metal polish. These products have just a touch of abrasiveness but still are gentle enough that they won't damage your acrylic surface. Put a dime-sized drop of polish on a clean cloth and rub the scratch gently in a circular motion.
Slightly deeper surface scratches or burnt spots
Wet a piece of #1500 grit sandpaper and rub the scratch or burnt spot in a circular motion; then use the liquid polisher or metal polish as described for very fine surface scratches or dulling.
Deep scratches and gouges
There are a few different bathtub repair kits readily available at your local home improvement store. Read the labels carefully to make sure you get one that best suits your needs. Follow the directions with your kit to prepare the filler paste, and then fill the crack using your finger or a wooden craft stick. Wait for the filler to dry. You can use a hair dryer to help speed up the drying process. Use #100 grit sandpaper to get the dry filler even with the surrounding surface. Then use gradually finer wet sandpaper to polish the finished surface, or a rubbing compound if supplied with your kit. If needed, match the paint supplied to your surface by mixing as directed. Allow the paint to dry 24 hours before using the bathtub.
Very deep scratches and gouges
For these, a sharp tool such as a utility knife, grinding tool or putty knife will be used to cut out the damaged surface. Be sure to cut in a V-shape to make it easier to fill with the filling paste. Sand the surface down with #100 grit sandpaper and then follow the directions for deep scratches and gouges.
Very old and/or damaged surfaces
Sometime the damage to your surface extends into the fibreglass beneath, or may just be too extensive to be worth repairing. For these situations, consider a bathtub liner. These are still less expensive than a complete replacement, and the results look professional.