I need help for this exercise:
Crumple zones in cars increase the time and the distance over the which a car stop during a collision. The length of the crumple zone is 1.6m.
a) Find the maximum speed that the car could have when hitting a wall head-on without subjecting the passager to an acceleration of more than 46.2g (i. e., 46.2 times the acceleration due the gravity)
b) How long would that collision last?

Explanation:

By increasing the time and the distance over which a car stops during a collision, the change in the velocity (acceleration) is reduced, reducing, in consequence, the impact.

The equation to determine the change in velocity for a uniformly accelerated motion is given by the relation between the speed, the distance, and the acceleration:

The acceleration must be less than or equal to 46.2g, which is 46.2 × 9.8m/s² = 452.76m/s². Thus, the condition is acceleration ≤ 452.76m/s²

Here, using the maximum acceleration:

Thus:

To determine the time use the impulse notion.

Since the final velocity is 0 (the car stops), Δv is the speed of the car: Δv = v.

Substitute:

terd muffin is the correct answer