The damage in this photo is superficial - just a gelcoat scratch although you can see the fiberglass underneath the gelcoat.
Unless there is evidence of damage to the fiberglass (leaking, local soft spot when pushing on it, splintering of the glass, or a white line on the inside of the hull) all you need to do is patch the gelcoat on the outside, and there is no rush to do this repair. You could wait until you have some free-time, or wait until you have several such scratches and fix them all at once, or make a party out of it and have friends bring their kayaks over to be touched up. As a temporary fix you could of course cover it with duct tape, but better would be Tear Aid tape, or even packaging tape.
When it's time to do the work, the healthiest and least messy procedure would be to do this outdoors. A clear, calm day with a temperature around 70 F would be ideal. For best results use gelcoat of the same color. With gelcoat you will need to mix in a catalyst to cure it. If you use gelcoat that says it is "Finish" or "With Wax" you can paint it on and it will harden completely. However most gelcoat is for laminating (if it doesn't say "Finish" or "With Wax" then it is for laminating) like when building a kayak. With laminating gelcoat unless you add "wax" (polystyrene) or cover the repair with wax-paper or plastic film while curing, the outside will remain tacky forever. For flat surfaces like the scratch in the photo I use wax-paper and some masking tape to temporarily cover the patch until cured. I'll also put masking tape on either side of the scratch to limit the overlap of my patch and reduce the sanding work that comes later. For small scratches like this I use a toothpick to apply the gelcoat. For bigger areas you can use a cheap paintbrush like little "Acid Brushes" sold for car touch-up repair work.
Fiber-lay or Tap Plastics have gelcoat and catalyst. Harbor Freight Tools has paint brushes and sand paper.
After the gelcoat sets (cures) you could call it good right there. The scratch is sealed, the under layer fiberglass is UV protected, everything is all one color, it just isn't smooth or like new but who cares right?. Or depending on how fussy you want to be, you could sand the patch and polish it with rubbing compound until it looks like new.
To make it look like new will take a variety of sand paper grits and rubbing compound grits and a buffing wheel for the rubbing compound. I usually just sand the patch till it is flush with the surrounding area and call that good. Sanding will scuff up the surrounding area; so it makes for a bigger blemish unless you go all the way to polishing everything out with rubbing compounds. In any case use a sanding block and start with about 180-220 grit sandpaper to get the patch fair and try not to sand any more of the surrounding area than necessary. Progress to finer and finer sandpaper with all the increments you can buy until about 2000 grit wet/dry sandpaper. Now it should look smooth and flair it just has a dull finish. Again you could call this good enough, but if you want to make it like new then you'll need a buffing wheel and rubbing compound. Like sandpaper, rubbing compound is available in different grit sizes and for the best result you'll need Course, Medium, and Fine (or Finishing) rubbing compounds.
Before investing in rubbing compounds and buffing wheels, make sure your gelcoat is a perfect color match. There are about 30 shades of white gel-coats and on older boats the the gelcoat fades or yellows so you can never get it completely matched. If you polish the repair you will see the difference in the colors more than if you leave it in the sanded dull finish.
For details on mixing the catalyst etc. try searching Google or YouTube.
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