help with physics problem
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This phyics problem is part of an optional homework assignment. You get like 10 extra credit points for completing the 10 problems plus it's good review for the test I'm having. I keep on solving it but my anser is wrong.
Here's the problem:
What should be the spring constant k of a spring designed to bring a 1200kg car to rest from a speed of 100 km/h so that the occupants undergo a maximum acceleration of 5g?
My approach is as follows:
100km/hr is 27.777... m/s. 5g's is (5x9.8)=49 (m/s^2). So the Kinetic energy of the cart will be canceled out by the spring force, or
.5(m)(v2) = .5(k)(x2)
Therefore, in order to find x, you need to set the decceleration =49.
d (or x in this case) =
[(final velocity)^2- (initial velocity)^2] / (2 x acceleration)
= [(0)-(27.777...)^2] / 98=7.87 m.
When I plug this value with all of the knowns back into the first equation, I get a k of 14 937.8 while the correct answer is about 3700. Anyone know what I did wrong?