HELP PHYSICS SHORT QUESTION!!!!!!!!!!!!!!!!only one question :)?

Question

What should be the spring constant k of a spring designed to bring a 1200 kg car to rest from a speed of 95 km/h so that the occupants undergo a maximum acceleration of 5.0 g?
=.........N/m

Answer 1

You have the mass of teh car, m, it's speed v, and the max acceleration a. Now

F =ma = kx where x = distance required to stop car.

Conservation of energy gives:

1/2kx^2 = 1/2mv^2 Use force relationship to solve for x:

x = ma/k

Then conservation of energy becomes:

1/2 k m^2a^2/k^2 =1/2mv^2

ma^2/k = v^2 solve for k

k = ma^2/v^2

Convert km/hour to m/s and plug in.