Final answer:
The amount of work required to stop a cart if it stopped at half the distance would remain the same, as it is reliant on the dissipation of the cart's kinetic energy, which does not change with distance.
Step-by-step explanation:
The question pertains to the work required to stop a cart if it stopped at half the distance compared to a previous scenario. In physics, the work done on an object is calculated as the force times the distance over which the force is applied (Work = Force × Distance). When initially dealing with the concept of work, it is important to note that stopping a cart involves kinetic energy which is proportional to the square of the velocity (KE = ½ mv²).
If the stopping distance is halved, assuming the same decelerating force is applied, it implies that the same amount of kinetic energy must be dissipated over a shorter distance. This would require a greater force to be applied over that distance to stop the cart in half the time. Therefore, the straightforward answer of work being twice as great or four times as great is not correct because the work required to stop the cart is not just about the distance but also involves the kinetic energy, which remains the same. So, the work done would remain the same since the energy to be dissipated (kinetic energy) has not changed.