Modeis subjected to complicated input functions often need to be solved numerically, even if they are linear. For example, the following is a model of the speed of a rocket$-$powered ground vehicle where the rocket's thrust f$($t$)$ is given by the following experimentally$-$derived tablie. The units are British Engineering.

$50$i$=$f$($t$)-30$v

$\backslash$table$[[$s$,$f$($t$)($b$)],[$t$($s$),$f$($t$)($b$)],[,],[0,0],[5\mathrm{.}5,11],[500,],[0\mathrm{.}5,500],[6\mathrm{.}0,11],[900,],[1\mathrm{.}0,700],[6\mathrm{.}5,12],[000,],[1\mathrm{.}5,1\mathrm{.}900],[7\mathrm{.}0,11],[500,],[2\mathrm{.}0,1\mathrm{.}500],[7\mathrm{.}5,10],[000,],[2\mathrm{.}5,2],[400,8\mathrm{.}0],[8,000],[3\mathrm{.}9,3],[600,8\mathrm{.}5],[6,000],[3\mathrm{.}5,5],[000,9\mathrm{.}0],[2,800],[4\mathrm{.}0,1],[000,9\mathrm{.}5],[1,000],[4\mathrm{.}5,9\mathrm{.}100],[10\mathrm{.}0,0],[,],[5\mathrm{.}0,10\mathrm{.}800],[,],[,]]$

Assuming the vehicle starts from rest, use a numerrical method to plot the vehicle's speed versus time for t Also plot the thrust versus time. In your simulation, assume the thrus: f$($r$)=$ a straight line connecting the data promts. Yos sam use the folliowing formule.

f$($t$)=($f$($t$\_($i$+1))-$f$($t$))/(0\mathrm{.}5)($t$-4.)+$f$($x$)$