Finding how long a collision lasts

[Ghost4512]

Homework Statement

In a crash test, a truck with mass 2000 kg traveling at 23 m/s smashes head-on into a concrete wall without rebounding. The front end crumples so much that the truck is 0.67 m shorter than before.

Homework Equations

About how long does the collision last? (That is, how long is the interval between first contact with the wall and coming to a stop?)
Δt = (c) What is the magnitude of the average force exerted by the wall on the truck during the collision?
Fwall, avg = N(d) It is interesting to compare this force to the weight of the truck. Calculate the ratio of the force of the wall to the gravitational force mg on the truck. This large ratio shows why a collision is so damaging.
[Fwall, avg]/mg =

The Attempt at a Solution

Well I figured out that the Average velocity during the collision was 11.5 m/s. But after this I am stuck.

 

[paisiello2]

Ok, how far does the rear bumper travel during the collision?

 

[Ghost4512]

Wouldn't it have only traveled .67 m?

 

[paisiello2]

Yes, so now can you solve for Δt?

 

[Ghost4512]

Oh, duh. Thanks.

 

[haruspex]

Yes, so now can you solve for Δt?

Not so fast, literally.
The speed will not be constant. The acceleration will not be constant either, but you will have to assume a particular time profile for the acceleration in order to solve the problem. The questioner probably expects you to assume constant acceleration.

 

[paisiello2]

I believe the OP did this already.

 

[Ghost4512]

Yep.

 

[haruspex]

O

Yep.

Ok, but my point is that to do this you had to make an assumption that was not only unjustified but in practice likely to be false.