You are traveling in a car at 72.0 km/h when the car is involved in an accident

Question

You are traveling in a car at 72.0 km/h when the car is involved in an accident that brings you and the car to a stop. Assume that your mass is 45.0 kg.

(a) What is your kinetic energy before the accident? (J)

(b) If you are wearing your seat belt, you come to rest after you and the car move through a distance of 1.50 m. What is the magnitude of the average force exerted on you (mostly by the seat belt) as you are slowing down? (N)

(c) What is the magnitude of your average acceleration as you are slowing down? Express this in units of g, assuming g = 10.0 m/s2. Note that anything over 5g may cause you to lose consciousness.

(d) If you are not wearing a seat belt, you may come to rest after striking the windshield and moving through a distance of 10 cm, instead. What is the magnitude of your average acceleration in this case? Again, express this in units of g.

Explanation / Answer

a) 72 km/h = 20m/s

kinetic energy before accident = 1/2 mv2

= 1/2(45)(20)2 = 9000 J

b) work done by force N = change in energy

f.d = 1/2mv2 - 0

f X 1.5 = 9000

f = 6000 N = 6 kN

c) f = ma

so a = f/m = 6000 / 45

a = 133.33 m/s2 = 13.3g m/s2  

d) then d = 0.10m

so f = 9000 / 0.10 = 90 kN

a = 90,000 / 45 = 2,000 m/s2 = 200g m/s2

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