Answer
The cart of mass 2m will accelerate at half the rate of the less massive cart of mass m.
Work Step by Step
Apply Newton's second law. The spring does not accelerate, and feels a zero net force. Each cart exerts the same amount of force on the spring, though oppositely directed.
Now, by Newton's third law, the spring exerts an equal force on each of the carts. Since the car's masses differ, their accelerations will differ, according to a = F/m. The double-mass car has half the acceleration of the other car.
