Elastic potential energy - different methods, different results

[Iamconfused123]

Homework Statement

A car of mass 1000 kg hits the spring with a speed of 10 m/s and condenses it by 1 m. If we disregard the friction, what is the resistance constant of the spring?

Relevant Equations

$E_p=\frac{kx^{2}}{2}$, $E_k=\frac{mv^2}{2}$

Can someone please tell me where I am wrong?
I tried to solve the problem using velocity equation; $v_{f}^2= v_{i}^{2} + 2as$ and got a= 50m/s^2, F= 50 000N and therefore F=kx -> k=50 000N/m because dx=1.

But it's not correct. When I do it using conservation of energy I get 100 000N/m. Which is correct according to the solutions.
$\frac{mv^2}{2}=\frac{kx^2}{2}$ -> k=100 000N/m.

Thank you.

 

[Hill]

Can someone please tell me where I am wrong?

Your first calculation is based on assumption of a constant acceleration / constant force. This assumption is incorrect.

 

[Iamconfused123]

Your first calculation is based on assumption of a constant acceleration / constant force. This assumption is incorrect.

Thank you very much. Just figured, Ep is proportional to the square of the elongation of the spring.