Final answer:
Airbags reduce the force required to stop a passenger in a collision by increasing the time over which the force is applied. Impulse, the product of force and time, remains constant, and the extended time from airbag deployment results in a lower stopping force compared to a collision with the dashboard.
Step-by-step explanation:
The concept involved in comparing the forces required to stop a moving passenger during a collision is impulse. Impulse is the product of the net force and the time over which it acts, and it is equal to the change in momentum. Given that the momentum change is constant, applying a force over a longer time period will result in a smaller force required to bring the passenger to a stop. An airbag deploys to extend the time over which the force acts on a passenger compared to the shorter time if the passenger were to hit the dashboard.
Using the formula for impulse, where impulse (I) equals the net force (Fnet) times the time interval (Δt), it is apparent that to achieve the same impulse, if the time increases, the force decreases, showcasing an inverse relationship (Fnet = I / Δt). Therefore, the force required to stop a passenger in 0.75 s with an airbag is significantly lower than the force required in 0.026 s with a dashboard. This is why airbags are an essential safety feature in vehicles, as they significantly reduce the forces experienced by passengers during collisions.