To determine how the speeds of the two carts would be affected by their masses, we can apply Newton's second law of motion: F = ma, where F is the force applied, m is the mass of the object, and a is the acceleration of the object.
In this case, the student applied a force of 200 Newtons to both carts. Since the force applied is the same for both carts, the acceleration of each cart would be directly proportional to the mass of the cart. In other words, the cart with the smaller mass would experience a larger acceleration, and therefore, move faster than the cart with the larger mass.
Using the equation F = ma, we can rearrange it to solve for acceleration (a): a = F/m.
For the cart with a mass of 100 kg:
Acceleration = 200 N / 100 kg = 2 m/s²
For the cart with a mass of 50 kg:
Acceleration = 200 N / 50 kg = 4 m/s²
Thus, the student would expect the cart with a mass of 50 kg to move faster than the cart with a mass of 100 kg.