As a $6000-$kg training plane lands on an aircraft carrier at a speed of $180$ km$/$h$,$ its tail hooks into the end of an $80-$m long chain which lies in a pile below deck. Knowing that the chain has a mass per unit length of $50$ kg$/$m and assuming no other retarding force, use a computational software to determine the time, velocity and deceleration of the plane when it travels a distance of $80$ m after landing and pulling out the chain.

The following tasks are required to achieve the objective

Use the computational software of your choice, do the following tasks:

$2.[40\%]$ Derive the necessary equations to generate the data and plotting.

$3.[20\%]$ Generate a table containing x$,$t$,$v and a for x$=0$ to $80$ m $.$

$4.[20\%]$ Plot a$-$x$,$v$-$x and t$-$x for x$=0$ to $80$ m $.$

All work must be done using the computational software. No hand$-$written work is allowed.