Given the GM$5$ model below with $m=1,n=2,$ and ${}_i=0$ :

$a_i(t+{}_i)=\frac{[v_i(t+{}_i){]}^m}{[x_{i-1}(t)-x_i(t){]}^n}[v_{i-1}(t)-v_i(t)]$

Derive its corresponding fundamental diagram, and calculate the free$-$flow speed, jam density

and capacity. Show the detailed calculation process.