Don't rush out to buy a new sink because of a minor blemish. Replacement costs are fairly high, costing upward of £97. Repair costs are considerably less--you can pick up a kit for around £13. Acrylic sinks have a solid surface, not sprayed or painted. This makes repairs easy to do.
Cut out the damaged acrylic of the sink in a V-shape with the utility knife. This will even out the sides of the chip and make the paste easier to apply. Don't cut through the fibreglass beneath the acrylic surface.
Prepare the acrylic repair kit's filler paste per the directions with the kit.
Put the filling paste on the chip and rub it in with your finger. Try to get it as smooth and even as possible so minimal sanding will be required. Wait an hour for the filler to dry.
Rub with dry 100-grit sandpaper in a circular motion to get the dry filler paste to be even with the surrounding surface.
Wet the 1500-grit sandpaper with water and rub 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.
Prepare the paint mix provided in the repair kit per the directions included, if painting is needed to match the black of the sink. Allow the paint to dry 24 hours before using.
You can use a hair dryer to help speed up the drying process. Look for a repair kit that has been factory colour matched if possible. The repair kit may be labelled as a tub repair kit, but the acrylic used on tubs is the same as that used on sinks.