Finding time of a collision using impulse and conservation of momentum

[Kaon]

Homework Statement

The front of a 1400 kg car is designed to absorb the shock of a collision by having a "crumple zone" in which the front 1.20 m of the car collapses in absorbing the shock of a collision.

(a) If a car traveling 25.0 m/s stops uniformly in 1.20 m, how long does the collision last?
answer in s

NOTE: I know this is not part of the template, but I needed to put it in somewhere. I realize this problem can be easily solved using kinematics equations and constant acceleration, but I'm trying to figure out why using the impulse doesn't work. See attempt section for more.

Homework Equations

vf = vi + at
vf² = vi² + 2ax
I= m$$\Delta$$v
I= m(vf) - m(vi)

The Attempt at a Solution

CORRECT ANSWER:
0= 25 + at
0= 25² + 2ax
a = -25²/2ax = -260.4 m/s²
t = -25/a = 0.096 s

TRIAL USING IMPULSE:
I = 0 - m(25) = -35 000
I = m$$\Delta$$x/$$\Delta$$t *I realize this may be where the problem lies
1.2m/-35 000 = t
t = 0.048 s *I also notice that this is exactly 1/2 of the right answer

 

[Mindscrape]

The thing is that there isn't much point in trying to use impulse for this problem. If you knew the force acting on the object as well as its starting velocity, impulse would be the way to go. Without knowing the force though, you would have to find it with kinematics, at which point you might as well also just use kinematics to correctly solve the problem.

Also, yes, the problem you had in your trial was doing
I = m∆x/∆t
Impulse is defined as
I= ∆p = m∆v = m(v2-v1)
where v2 and v1 are instantaneous velocities at particular times. You used an average velocity with ∆x/∆t.

 

[Kaon]

Thanks, I think I understand. I somewhat knew that I was working in circles, but not knowing why I couldn't get the answer was bugging me to no end.