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 ( ), defined as =5/2 . In the expression, is the duration of the accleration, but is not equal to the acceleration. Rather, is a dimensionless constant that = the number of multiples of that the acceleration is equal to. In one set of studies of rear-end collisions, a person's velocity increases by 13.7 km/h with an acceleration of 36.0 m/s2 . Let the + direction point in the direction the car is traveling. What is the severity index for the collision?