Final answer:
Impulse is the mathematical concept used to analyze the force during a collision, where increasing collision time with safety features reduces the force on passengers.
Step-by-step explanation:
The mathematical concept that can be used to analyze the force experienced by passengers during a collision is impulse. Impulse is the product of the net force applied during a collision and the time duration over which the force acts. The formula for impulse is given by Impulse (J) = Net Force (Fnet) × Time (Δt). This concept is crucial in automobile safety because increasing the collision time with features like airbags and crumple zones reduces the force experienced by passengers, thereby reducing injuries. It's important to note that while the momentum change of the occupants is the same, the force exerted on them is less if it acts over a longer period.