Very large accelerations can injure the body, especially if they last for a cons

Question

Very large accelerations can injure the body, especially if they last for a considerable length of time. The severity index (SI), a measure of the likelihood of injury, is defined as SI = a5/2t, where a is the acceleration in multiples of g and t is the time the acceleration lasts (in seconds). In one set of studies of rear end collisions, a person's velocity increases by 12 km/h with an acceleration of 35 m/s2.

(a) What is the severity index for the collision? (s)

(b) How far does the person travel during the collision if the car was initially moving forward at 7.0 km/h? (m)

PLEASE SHOW WORK

Explanation / Answer

PART A

u + (12*1000/3600) = u + 35*t

t = 0.095

a = 35/9.8 = 3.571

SI = a5/2*t = 2.289 s

PART B

u = 7 km/hr = 1.94m/s

v2 = u2 + 2as

s = (3.33)2 - 1.942/(2*35) = 0.1046 m

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