Final answer:
Hitting a haystack is safer because it extends the time over which the impact occurs, thereby reducing the force on the car and passengers due to the principle of impulse.
Step-by-step explanation:
When considering why hitting a haystack is safer than hitting a brick wall with a car with faulty brakes, it's important to understand the concept of impulse. Impulse is the product of the net force and the time over which it acts (Fnet Δt). In the case of a collision, although momentum changes to zero irrespective of what the car hits, the crucial difference lies in the duration of the impact.
Hitting a haystack is safer because it increases the time taken to come to a stop compared to a brick wall. This longer duration reduces the net force exerted on the car and its occupants due to the inverse relationship between force and time when momentum change is constant. This principle explains why vehicles have safety features like airbags and crumple zones designed to extend the collision time and minimize injury during accidents.