Final answer:
Increasing the time interval over which a force is applied to stop a moving cart requires a smaller force to achieve the same change in momentum, as shown by the impulse-momentum theorem.
Step-by-step explanation:
If a force is applied to stop a moving shopping cart, increasing the time interval over which the force is applied will require a smaller force to achieve the same change in momentum. This principle is illustrated by the usage of safety features like airbags and seat belts, which extend the time over which the force acts on passengers during a sudden stop, therefore reducing the force required to change their momentum. According to the impulse-momentum theorem, the change in momentum (Δp) of an object is equal to the net force (Fnet) applied to it times the time interval (Δt) the force is applied: Fnet = Δp/Δt. Hence, if Δp remains constant and Δt is increased, Fnet must decrease.