Don't rush out to buy a new bathtub because of a minor blemish. Replacement costs are fairly high, and repair costs are not. Acrylic bathtubs have a solid surface, not a sprayed or painted on finish. This makes repairs rather easy to do.
Cut out the damaged area of the tub in a V-shape with the utility knife.
Prepare the bathtub repair kit's filler paste per the directions included with the kit.
Put the filling paste on the crack and rub it in with your finger. Get it as smooth and even as possible so minimal sanding will be required. Wait an hour for the filler to dry.
Rub the filled crack with dry #100 grit sandpaper in a circular motion to get the dry filler paste even with the surrounding surface.
Wet the #1500 grit sandpaper with water and rub the tub in a circular motion to polish the finished surface. Sometimes the repair kit will come with rubbing compound to be used with a clean cloth instead.
Paint the surface if needed. Prepare the paint mix provided in the repair kit per the directions included. Paint using a brush or sponge, depending on your preference. Allow the paint to dry 24 hours before using.
You can use a hair dryer to help speed up the drying process.