Cart moves whenever I apply any force to it

There might be a couple issues.
The parts of the cart or tracks might have a Velocity in them already. Check the AssemblyLinearVelocity in all the components.
Another problem could be that if you used MeshParts or Unions for the wheels their shape might not be perfectly round because the flange and wheel would make a convex shape. Cylinders or Ball shaped Parts are best for any rotating parts. You can check out this plugin Mesh Optimization Tools - Roblox to see what the actual physcial shape of your meshes/unions are. If you set the CollisionFidelity property to Precise it may work out, but usually there are small wedges/flat areas that don’t work well as wheels.

Most cart systems also use Parts under and between the rails to keep them on the tracks.
Here’s a post I made a train model for a while ago to help out. How to make a basic train - #12 by Scottifly

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