Answer
0.11 m
Work Step by Step
Apply the principle of conservation of mechanical energy. The kinetic energy of the car is later stored as potential energy in the bumper. At the beginning there is no PE and at the end there is no KE.
$$\frac{1}{2}mv^2=\frac{1}{2}kx^2$$
$$x=\sqrt{\frac{m}{k}}v=\sqrt{\frac{1300kg}{410000N/m}}(2.0m/s)\approx 0.11m $$