What kind of vehicle is this?
I'd start with a *very* thorough decon of the area. Tar remover, iron remover, heavy wash with a good detergent, clay it, and a prep spray wipedown so you can really see what you're dealing with. Lots of scratches on white paint appear like what you have in the pic, but sometimes can just be stubborn contamination. You said it's from a shopping cart, it may even just be color transfer from the cart itself.
Once you've determined they're actually scratches, Mike's advice is a good first step. For me, I'd go with a medium cut polish on a MF hand applicator first. Something like Jescar medium polish, Meg's #83, Griot's correcting cream etc. Only after you determine these are not enough would I then step up in product cut. Jescar compound would be my product of choice here, but M101 or 105, Menzerna 400, Griot's FAST correcting cream, or Carpro Clearcut would be the way to go here. If compound doesn't get it, you'd be looking at wetsanding but only after thorough paint measurements have been taken and only if it's within your comfort zone.
Being that the impact appears to have occurred on the peak of the body line, I don't think the machine really buys you anything in terms of speed or convenience. Elbow grease will be the way to go.
