# Calculating deceleration .need quick help, please

## Homework Statement

Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1000 m/s2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.36 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.1 mm. If the floor is carpeted, this stopping distance is increased to about 1.1 cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume that the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate.

## Homework Equations

I used v(final) = v(initial) + at ------> equ 1

## The Attempt at a Solution

I solved for initial velocity using

final v (0) = initial v + 2 a delta x

and then substituted that in equ 1. But apparently my answer is wrong.

Any advice is greatly greatly appreciated! Thanks!!

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rl.bhat
Homework Helper

Hi niisama, welcome to PF.

inal v (0) = initial v + 2 a delta x

This equation should be

initial v^2 (0) = initial v^2 + 2 a delta x

Now work out.