Finding the spring constant of a accident safety system

[Revan718]

Homework Statement

An accident safety system uses a spring to absorb the energy of a car before the car collides with a bridge abutment.
The vehicle has a mass of 1000kg and the design calls for stopping a car moving at 5m/sec (11.2 mi/hr) in 0.5m.
Find the spring constant k

Homework Equations

F=kx -> k=F/x

The Attempt at a Solution

I am having trouble finding the force of the collision. It is needed to find k, is it not? I was thinking I may need to use a kinematics equation to do this and solve for the acceleration (deceleration in this case).

 

[Revan718]

I tried using the equation:
v^2=v(0)^2+2a(s-s(0))
and solved for a, resulting in a=25m/s^2
Is this correct?

 

[Revan718]

I tried using the equation:
v^2=v(0)^2+2a(s-s(0))
and solved for a, resulting in a=25m/s^2
Is this correct?

Shouldn't the acceleration be negative?

 

[nvn]

Nice work, Revan718. Acceleration is negative.