$18$

$7.$ Simulate the car following behavior for the following situation using a system update $($or scan$)$ of $0\mathrm{.}5s$ upto $3\mathrm{.}0s.$ Two vehicles are moving at an initial speed of $16\frac{m}{s}$ and the distance headways are $28m.$ At $t=1s,$ the lead vehicle $($LV$),$ accelerates at $1\frac{m}{s^2}$ for $2s$ and from $t=3s,$ the $LV$ decelerates at $-1\frac{m}{s^2}$ for $2s.$ Assume a perception reaction time of $1s$ and GM$5$ model for the following $l=1,m=0,{}_{1,m}=13\frac{m}{s}.$

$(5)$