REPAIR - Bathtub caulking or grouting between acrylic bathtub and tile
OK, grout should never have been used there in the first place because it will crack. I can see more cracking from your pictures. Your best bet is get as much of that grout out of there as you can as it will continue to crack and fall out. Once you get the grout out, get some quality silicone caulk and run a good bead of caulk around the tub. Make sure everything is dry before caulking.