This is surprisingly slick:
The real trick would be to levitate the “train” within the coil reducing contact to just an electrically conductive brush, vastly reducing friction and speeding the thing along. I’m not sure how to do that on a budget.
This video openly swipes the idea, but at least goes to the bother of explaining the physics involved:
This would seem to be a good possibility for a kids science experiment (they still do that, right?). A particularly industrious kid might consider replacing the battery with something of the same size, but much greater power: some sort of generator perhaps, driven by a tiny combustion engine or some such. Or put a PV cell on it and aim a dangerously powerful laser beam at it. Consider changing the shape of the coil… instead of winding it around a cylinder, try square stock. Then put a simple flat low-friction track on the bottom inside the square coil, and put wheels on the “car.” A truly industrious kid would embed the coil within a rigid ceramic shell backed up by a carbon fiber wrap, and replace the low power batteries with insanely powerful capacitors. The burst of energy and acceleration would be very quick, but done right the “car” might project down the barrel with considerable authority. Go further and build a box magazine to hold the little electromagnetic projectiles, a hand-held aiming and trigger mechanism, a Picatinny rail to mount laser sights… then bring to school and show the class. That’ll be fun for everyone.