Passenger in a vehicle that is struck from behind can suffer whiplash injuries t

Question

Passenger in a vehicle that is struck from behind can suffer whiplash injuries to their neck ligaments and cervical spine with accelerations as low as 3.5g. Consider a scenario where a large truck strikes a small car from behind in a comletely inelastic rear-end collision that lasts 0.2 seconds. The truck and car have masses of 3000 kg and 1000 kg, with initial speeds of 25 m/s and 10 m/s repectively. The speed difference is roughly equal to 34 mph and would normally be regarded as a "moderate speed" collision. What is the average acceleration that would be exprienced by the occupants of the small car during this collision, and would they be vulnerable to whiplash injuries?

Explanation / Answer

v=d/t
a=v/t

v=velocity in m/s
d=distance in m
a=acceletration m/s2

average velocity (before crash and after crash is (34+0)/2 = 17

crashing time is t = d/v = 0.82/17 = 0.048 seconds

so acceleration a = ((34-0)/0.048) = 708m/s2

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