Answer
The momentum of the plastic cart will be less than the momentum of the lead cart after traveling a distance of one meter.
Work Step by Step
Equal forces are used to push both carts for a distance of one meter. Since the plastic cart has less mass, it will have a greater acceleration and reach one meter in less time.
Since the force acts for a shorter time on the plastic cart, the impulse exerted on the plastic cart is less than the impulse exerted on the lead cart. Therefore, the change in momentum of the plastic cart is less than the change in momentum of the lead cart.
Since both objects started from rest, the momentum of the plastic cart will be less than the momentum of the lead cart after traveling a distance of one meter.