I have just tried a momentum question involving springs. I got the wrong answer and the method used in the solution is different, but i still do not see what i did wrong.

The question is: a railway engine 6.2*10^4 and a carriage 4*10^4 have coupled. They have hit a buffer spring (to stop them) from an initial speed of 0.15m/s. Assuming the buffer behaves like a spring of stiffness 320kN/m calculate the maximum compressiion of the spring.

**The solution given is:**

Kinetic energy of train :

0.5 × 10.2 × 104 × 0.152 = 1150 J

0.5* F e

= 0.5× (k e) × e = 0.5 × k e^2

0.5 × 320 × 103 e2 = 1150 1

**gives compression e = 8.47 × 10^-2 m**

**My Solution**

*F=Change in MV/Change in time F= Ke*

so:

MV/T = Ke

s= ((u+v)/2)t Therefore : t=(40/3)e

so Mv= 40/3(Ke^2)

And i calculate e=0.059 m

But this is different to the solution given, why does my method not work?

Thanks