How to cut the rope? We have two cars and a rope, made using cloth simulation, that is stretched between them. These cars are moving in opposite directions to each other. The rope should be tensioned when the cars start moving, and then it should be pulled away from one of the cars.

I can make the rope, using cloth simulation, select the vertices at the ends of the rope and add pinning, and then vertex parent them to the cars. But how can I make this tearing of the rope?
Make a vertex group for each end of the rope and use a hook modifier to attach it to each car.  As you animate the car to move backward the rope will tighten with the cloth sim.  To release it just set a keyframe to set the object to none making the rop fall.