Write a python script

Required Libraries:

math

The velocity of an object is a function of time $(t)$ and is given by the function:

$V(t)=\sqrt[3]{4t^3+\frac{1}{2}{t}^2+2t+100}[\frac{(m)}{(s)}]$

where $t$ has units of seconds.

a$)$ Determine the values of velocity for $t=0,0\mathrm{.}25,0\mathrm{.}5,0\mathrm{.}75,$ and $1$ sec using Python command window as a calculator. Round the values to $4$ digits after the decimal place and list the values in a comment $($or comments$)$ in the Task $1$ section of your Python file. Make sure to explain the values in the comment$($s$).$

b$)$ Define an array named $t$ that contains values of time starting with $0$ seconds and ending with $10$ seconds with increments of $0\mathrm{.}25$ seconds.

c$)$ Using a for loop, determine the velocity of the object at each value of $t$ and store the result in an array named velocity. $($Check to make sure that the first five elements in velocity equal those determined earlier using a calculator.$)$

d$)$ Plot velocity as a function of time $(t)$ using a solid blue line. Label the plot axes and title the plot appropriately.

e$)$ Define variables for velocities at positions $1,2,3,4$ and $5$ of your velocity index and display as an output, comparing your results in the command window with the results from part a$.$