Question

When you blink your eye, the upper lid goes from rest with your eye open to completely covering your eye in a time of 0.024 s.

Answer 1

a) Distance moved by the top lid during a blink: 1 cm (estimate)

b) The acceleration is $34.7 m/s^2$

c) The final speed is 0.83 m/s

Explanation:

a)

For the purpose of this problem, we can estimate the size of the eye from the top lid to the bottom lid to be 1 cm, so this is the distance moved by the top lid during a blink.

b)

Assuming the motion of the eyelid to be at constant acceleration, we can find the acceleration by using the following suvat equation:

$s=ut+\frac{1}{2}at^2$

where

s is the distance covered

u is the initial velocity

t is the time

a is the acceleration

For the eyelid, we have:

u = 0 (it starts from rest)

s = 1 cm = 0.01 m is the distance covered

t = 0.024 s is the time taken

Solving for a, we find the acceleration:

$a=\frac{2s}{t^2}=\frac{2(0.01)}{0.024^2}=34.7 m/s^2$

c)

The final speed of the upper eyelid can be found by using another suvat equation:

$v=u+at$

where

v is the final speed

u is the initial speed

a is the acceleration

t is the time

For the eyelid in this problem, we have

u = 0

$a=34.7 m/s^2$

t = 0.024 s

Substituting, we find the final speed:

$v=0+(34.7)(0.024)=0.83 m/s$

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