Seat Belt constraints in a crashing car

[atbruick]

Homework Statement

A person who is properly constrained by an over-the-shoulder seat belt has a good chance of surviving a car collision if the deceleration does not exceed about 30 "g's" (1.0 g = 9.80 m/seconds squared).

Assuming uniform deceleration of this value, calculate the distance over which the front end of the car must be designed to collapse if a crash brings the car to rest from 80 km/h.

Homework Equations

The Attempt at a Solution

 

[gerben]

How long does it take to go from a speed of 80 km/h to 0 km/h, if the speed decreases by 30x9.80 m/s every second?
What distance would one travel if moving from stand still at acceleration 30x9.80 m/s in this time?

 

[atbruick]

For the first I got 22 m/s (instead of 80km/h) then divided that by 30*9.80m/s and got 0.075, which is the time it would take to go from 22 m/s to 0 m/s in the crash.

Then I found in that time frame a person could travel 1.65, or 1.7 meters. I hope these calculations are right; I entered 1.7 into the answer and it was wrong.

 

[lewando]

"30*9.80 m/s" (velocity) is not the same as "30*9.80 m/s per second" (acceleration)

There exists a specific kinematic equation that you should be using to get a better answer.

 

[gerben]

It appears you assumed that the car was going 22m/s the whole time during that 0.076 seconds, but the car is decelerating during that time.