Can anyone answer this physics question?

Question

Here is the problem that I am having a horrible time with:

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 0.40 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.0 mm. If the floor is carpeted, this stopping distance is increased to about 1.2 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.

Hardwood floor magnitude _______ m/s2
Duration _____ ms

Carpeted floor magnitude _______ m/s2
Duration _____ ms

Answer 1

First, calculate the velocity at impact.
We'll assume that air resistance is negligible, so the child is acted on by gravity which has an acceleration of 9.8m/s^2

using the d=at^2 equation

.4/9.8=t^2 the child falls for 0.202 s
that yields a velocity of 2m/s at impact
to find the deceleration, look at the distance traveled and calculate the time. We'll assume constant deceleration for both cases, which means the average velocity through the deceleration is 1m/s

Hardwood floor
2.0 mm, which is .002m
Duration=.002s or 2ms
magnitude = 1000m/s^2
This is twice the required impact to cause injury.

Carpet
distance 1.2cm =.012m
Duration =12ms
magnitude =170m/s^2
This is significantly less impact below the trauma level.