Serway & Jewett — Oscillatory Motion: Problem 10

To test the resiliency of its bumper during low-speed collisions, a 1 000-kg automobile is driven into a brick wall. The car’s bumper behaves like a spring with a force constant \(5.00 \times 10^6 \text{ N/m}\) and compresses \(3.16 \text{ cm}\) 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?