Barrier Deformation and Impact of Car

[depre87]

Homework Statement

Force exerted on a car by a crash barrier as the barrier crushes is F=-(4.5+140s) kN where s is the distance in metres from the initial contact. If a car of mass 2000 kg is traveling at 100 km/h when it hits the barrier the barrier deformation required to bring the car to rest will be most nearly: 0.35,1.04,1.78,2.81,3.29 metres

Homework Equations

Not entirely sure which to use here? Impulse => Fdt=mv1-mv0 or conservation of energy:
0.5mv^2+(F)ds = 0

The Attempt at a Solution

0.5mv^2+(F)ds = 0
0.5(2000)(27.78)^2+[-4.5s-70s^2] = 0, solve for s and i believe i got the incorrect answers (it is supposed to be 3.29m)

any clues guys am i completely off in my method? thanks!

 

[cepheid]

Your method looks fine. If you use the work-energy theorem, you get W = ΔK. To bring the car to rest, the final K must be 0, so W = 0 - K₀ = -K₀ where K₀ is the initial kinetic energy. Let S (capital) be the displacement of the barrier that is enough to bring the car to a rest. Then

$$-K_0 = W = \int_0^S F(s)\,ds = -\int_0^S (4.5 + 140s)\,ds$$

$$K_0 = 4.5S + 70S^2$$

After this, it's just a matter of plugging in the given values for S and seeing which one gets you closest to K₀. If you got it wrong, you must have an arithmetic error somewhere. What did you get for K₀?