If the car comes to a stop and compresses the spring by a distance x in the process, then the restoring force performs
W = -1/2 (2.0 × 10⁶ N/m) x²
of work on the car. By the work-energy theorem, this is equal to the change in the car's kinetic energy,
∆K = 0 - 1/2 (1500 kg) (25 m/s)²
Solve for x :
-1/2 (2.0 × 10⁶ N/m) x² = -1/2 (1500 kg) (25 m/s)²
x² = (1500 kg) (25 m/s)² / (2.0 × 10⁶ N/m)
x = √((1500 kg) (25 m/s)² / (2.0 × 10⁶ N/m))
x ≈ 0.68 m
