speed={20,25,30,35,40,45,50,55,60,65,70,75,80};
reactiondistance={22,28,33,39,44,50,55,61,66,72,77,83,88};
brakingdistance={20,28,40.5,52.5,72,92.5,118,148.5,182,220.5,266,318,376};

reactiondata=Transpose[{speed,reactiondistance}];
reactiongraph=ListPlot[reactiondata]

ruleofthumb[v_]:= 15 v/10
ruleofthumbplot=Plot[ruleofthumb[v],{v,0,80}];
Show[{reactiongraph,ruleofthumbplot}, PlotRange->All]

The rule of thumb works well if the two vehicles are following one another at the SAME speed (and the vehicle in front can not stop much faster). However, this is not a safe assumption.

Fit[reactiondata,{1,x},x]

reactionmodel[v_]:=1.1 v
reactionmodelplot=Plot[reactionmodel[v],{v,0,80}]

Show[{reactionmodelplot,reactiongraph}, PlotRange->All]

brakingdata=Transpose[{speed,brakingdistance}];
brakinggraph=ListPlot[brakingdata]

brakingdatamodel=Transpose[{speed^2,brakingdistance}]

brakinggraphmodel=ListPlot[brakingdatamodel]

Fit[brakingdatamodel,{1,x},x]

brakingmodel[v_]:=0.059 v^2
brakingmodelplot=Plot[brakingmodel[v],{v,0,80}]

Show[{brakingmodelplot,brakinggraph}, PlotRange->All]

stoppingdata=Transpose[{speed, reactiondistance+ brakingdistance}];
stoppingmodel[v_]:=reactionmodel[v]+brakingmodel[v]
stoppingdataplot=ListPlot[stoppingdata];
stoppingmodelplot=Plot[stoppingmodel[v],{v,0,80}];
Show[{stoppingdataplot,stoppingmodelplot}, PlotRange->All]

The safe assumption is that the trailing vehicle can fully stop in the distance between it and the vehicle in front. In this way, regardless of the speed of the lead vehicle, the trailing car will not crash into the vehicle in front of it.

newruleofthumbplot=Plot[Piecewise[{{5280v/3600,0≤ v<10},{2 5280v/3600,10≤v<40}, {3 5280v/3600,40≤v<60},{4 5280v/3600, 60≤v<75}}],{v,0,80}];
Show[{stoppingdataplot,newruleofthumbplot}, PlotRange->All]

Table[stoppingmodel[v],{v,{10,20,30,40,50,60,75,80}}]