Energy of a simple harmonic oscillator

1. Oct 31, 2011

shawli

1. The problem statement, all variables and given/known data

To test the resiliency of its bumper during low-speed collisions, a 1000 kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 5.00 x 106 N/m and compresses 3.16cm as the car is brought to rest. What was the speed of the car before impact, assuming no mechanical energy is transformed or transferred away during impact with the wall?

2. Relevant equations

I'm not really sure how to 'classify' this type of problem... But I tried to think of it in terms of total energy in an isolated system (I think that's what its called?)

Etotal = Ekinetic + Eelastic
1/2 kA2 = 1/2 m v2 + 1/2 k x2

3. The attempt at a solution

I have my equation:

kA2 = m v2 + k x2

But I'm missing the value for A.

And there is this piece of information... the car "compresses 3.16cm as the car is brought to rest", so v = 0 (of the car) when x = 0.0316m, which is then the max displacement for the spring. But... I'm not sure where to apply this information!

Any help is appreciated :)

Can you offer guidance or do you also need help?
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