### Understanding the Severity Index (SI) in Rear-End Collisions#### IntroductionVery large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge the likelihood of injury is the severity index (\(SI\)), defined as \(SI = a^{5/2} t\). In this expression, \(t\) is the duration of the acceleration but is not equal to the acceleration. Rather, \(a\) is a dimensionless constant that equals the number of multiples of \(g\) that the acceleration is equal to.#### Rear-End Collision StudyIn one set of studies of rear-end collisions, a person’s velocity increases by 17.5 km/h with an acceleration of 30.5 m/s\(^2\). Let the +\(x\) direction point in the direction the car is traveling. What is the severity index for the collision?\[SI = \boxed{2.71}\]#### Distance Travelled During CollisionHow far (\(d\)) does the person travel during the collision if the car was initially moving forward at 4.60 km/h?\[d = \boxed{\ \_________\ }\ m\]This section aims to educate students and individuals interested in understanding how to calculate and interpret the severity index (SI) in the context of vehicle collisions and the impact it has on the human body. Additionally, it explores the calculation of distance traveled by a car during such collisions.

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Description: ### Understanding the Severity Index (SI) in Rear-End Collisions#### IntroductionVery large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge the likelihood of injury is the severit

Given:- We know that the severity index SI = a5/2t. here t is the duration of acceleration but a…

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large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge the likelihood of injury is the severity index (SI), defined as SI = a a5/21. In the expression, t is the duration of the accleration, t. but a is not equal to the acceleration. Rather, a is a dimensionless constant that equals the number of multiples of g that the acceleration is equal to. In one set of studies of rear-end collisions, a person's velocity increases by 17.5 km/h with an acceleration of 30.5 m/s². Let the +x direction point in the direction the car is traveling. What is the severity index for the collision? SI = 2.71 How far d does the person travel during the collision if the car was initially moving forward at 4.60 km/h?

large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge the likelihood of injury is the severity index (SI), defined as SI = a a5/21. In the expression, t is the duration of the accleration, t. but a is not equal to the acceleration. Rather, a is a dimensionless constant that equals the number of multiples of g that the acceleration is equal to. In one set of studies of rear-end collisions, a person's velocity increases by 17.5 km/h with an acceleration of 30.5 m/s². Let the +x direction point in the direction the car is traveling. What is the severity index for the collision? SI = 2.71 How far d does the person travel during the collision if the car was initially moving forward at 4.60 km/h?

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ISBN:9781305952300

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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### Understanding the Severity Index (SI) in Rear-End Collisions

#### Introduction
Very large accelerations can injure the body, especially if they last for a considerable length of time. One model used to gauge the likelihood of injury is the severity index (\(SI\)), defined as \(SI = a^{5/2} t\). In this expression, \(t\) is the duration of the acceleration but is not equal to the acceleration. Rather, \(a\) is a dimensionless constant that equals the number of multiples of \(g\) that the acceleration is equal to.

#### Rear-End Collision Study
In one set of studies of rear-end collisions, a person’s velocity increases by 17.5 km/h with an acceleration of 30.5 m/s\(^2\). Let the +\(x\) direction point in the direction the car is traveling. What is the severity index for the collision?

\[SI = \boxed{2.71}\]

#### Distance Travelled During Collision
How far (\(d\)) does the person travel during the collision if the car was initially moving forward at 4.60 km/h?

\[d = \boxed{\ \_________\ }\ m\]

This section aims to educate students and individuals interested in understanding how to calculate and interpret the severity index (SI) in the context of vehicle collisions and the impact it has on the human body. Additionally, it explores the calculation of distance traveled by a car during such collisions.

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