...a nerve. These send signals from the body to the brain and vice versa.
To solve this problem it is necessary to apply the equations related to the description of the tangential and angular movement.
The displacement where the speed and acceleration is related is given by the equation:
![x = v_0t+\frac{1}{2}at^2](https://tex.z-dn.net/?f=x%20%3D%20v_0t%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2)
Where
Initial velocity (0 because start from rest)
t = time
a = Acceleration
We have angular acceleration but not tangential acceleration. Tangential acceleration can be obtained through the relationship
![a = r\alpha \rightarrow r = \frac{diameter}{2}](https://tex.z-dn.net/?f=a%20%3D%20r%5Calpha%20%5Crightarrow%20r%20%3D%20%5Cfrac%7Bdiameter%7D%7B2%7D)
![a = \frac{0.08}{2}(3)](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B0.08%7D%7B2%7D%283%29)
![a = 0.12m/s^2](https://tex.z-dn.net/?f=a%20%3D%200.12m%2Fs%5E2)
And we have also that the displacement is
![x = 6m](https://tex.z-dn.net/?f=x%20%3D%206m)
Now replacing,
![x = v_0t+\frac{1}{2}at^2](https://tex.z-dn.net/?f=x%20%3D%20v_0t%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2)
![6 = 0*t+\frac{1}{2}(0.12)t^2](https://tex.z-dn.net/?f=6%20%3D%200%2At%2B%5Cfrac%7B1%7D%7B2%7D%280.12%29t%5E2)
![6 = \frac{1}{2}(0.12)t^2](https://tex.z-dn.net/?f=6%20%3D%20%5Cfrac%7B1%7D%7B2%7D%280.12%29t%5E2)
![t = 10s](https://tex.z-dn.net/?f=t%20%3D%2010s)
Therefore will take the cord to unwind around 10s