Question

In the previous question ( about the 1 kg cart), if the cart stopped in half the distance, the force required to stop the cart would be?

1) half as great
2) the same
3) twice as great
4) four times as great

Answer 1

The force required to stop a 1 kg cart in half the distance is four times as great, due to the work-energy principle and the inverse square relationship between force and stopping distance.

Step-by-step explanation:

If a 1 kg cart stops in half the distance, the force required to stop the cart would be four times as great. This comes from the work-energy principle, which states that the work done by the stopping force is equal to the change in kinetic energy of the cart. When the stopping distance is halved, the force must do the same amount of work over a shorter distance, which requires an increase in the force. In fact, given a constant deceleration, the force is inversely proportional to the square of the stopping distance, meaning that if you reduce the stopping distance by half, the required force goes up by a factor of four.