Answer:
When an object is in motion, work is done on it to either increase or decrease its speed. The amount of work done on an object is equal to the change in kinetic energy it experiences.
For Car A:
Given that the car is moving at 5 m/s and comes to a stop, its initial kinetic energy is:
K.E. = 1/2 * mass * velocity^2
Since the car comes to a stop, its final kinetic energy is zero.
The change in kinetic energy is therefore: K.E. final - K.E. initial = -1/2 * mass * velocity^2
For Car B:
Given that the car starts from rest and moves to a velocity of 5 m/s, its initial kinetic energy is zero.
The final kinetic energy is: K.E. = 1/2 * mass * velocity^2
Comparing the amounts of work done on Car A and Car B, we find that the work done on Car A is negative since the change in kinetic energy is also negative, indicating that there is a decrease in kinetic energy. This means that work is done against the motion of Car A to bring it to a stop. On the other hand, the work done on Car B is positive, indicating an increase in kinetic energy as the car accelerates from rest to a velocity of 5 m/s.
Therefore, the amount of work done on Car A is greater in magnitude than the amount of work done on Car B, since the work done on Car A involves coming to a complete stop from an initial velocity of 5 m/s, while the work done on Car B involves accelerating from rest to a velocity of 5 m/s.