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)

a) The severity index (SI) is 3047.749, b) The injured travels 0.345 meters during the collision.

Explanation:

a) The g-multiple of the acceleration, that is, a ratio of the person's acceleration to gravitational acceleration, is:

The time taken for the injured to accelerate to final speed is given by this formula under the assumption of constant acceleration:

Where:

- Initial speed, measured in meters per second.

- Final speed, measured in meter per second.

- Acceleration, measured in .

- Time, measured in seconds.

Lastly, the severity index is now determined:

b) The initial and final speed of the injured are and , respectively. The travelled distance can be determined from this equation of motion:

Where is the travelled distance, measured in meters.

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