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 equals 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 12.1 km/h with an acceleration of 35.0 m/s2 . Let the + direction point in the direction the car is traveling. What is the severity index for the collision?

How far does the person travel during the collision if the car was initially moving forward at 5.80 km/h ?

On a cold day, when the air temperature is 0°c, you empty your lungs and take a deep breath, filling your lungs with 4.2 l of air. if you hold your breath until the temperature of the air in your lungs reaches 37°c, what is the volume of the air in your lungs at that point, assuming the pressure does not change?

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

Aman throws a football straight into the air. as it rises, it slows down. which type of energy is the football gaining?