$k=8.1 \times 10^4N/m$
Transcript for this Giancoli solutionWe know that the size of the change in kinetic energy for this car. So we're going to go up to the value of change in kinetic energy which is one half 'mv' initial squared, the final speed is zero because the car comes to a stop. So we don’t need that term in this difference, this subtracting the final from the initial. We can just write down the initial kinetic energy because it loses all that it had to begin with. Is equals the change in potential energy which is going to be the potential energy gained by the spring. So one half 'kx' squared. So we have one half 'mvi' squared equals one half 'kx' squared.
I'm putting these absolute value signs here just to say that negative signs don’t really matter as long as we keep in mind what's going on. What these are saying is that, the amount of change in kinetic energy equals the amount of the change in potential energy.
So we'll solve for 'k'. So dividing both sides by 'x' squared, and then noticing that one half is a common factor which cancels on both sides. Gives us 'k' is 'mvi' squared over 'x' squared. This is 1,200 kilograms times the speed which we'll have to change into meters per second. So we have 45 kilometers per hour divide by 3.6 to change into meters per second, square that and divide by2.2 meters squared. That’s ANSWER newtons per meters is the spring constant.