ClearAll;
$DefaultFont = {"Times-Roman",10};
Needs["Graphics`Graphics`"];
V1[t_]:= 5 (8779 + 70560 t - 924000 t^2 + 3136000 t^3 - 3360000 t^4)/432;
V2[t_]:= 2(810447 - 5630400 t + 14463600 t^2 - 15640000 t^3 + 6120000 t^4)/1127;
V3[t_]:= 4(661257 - 3118500 t + 5512500 t^2 - 4312000 t^3 + 1260000 t^4)/99;
testes1 = {{0,2.0}, {1,4.0}, {2,5.7}, {3,7.0}};
testes2 = {{3,7.0}, {4,5.8}, {5,4.9}, {6,3.7}, {7,2.5}, {8,2.2}, {9,2.3}, {10,2.6}, {11,3.9}, {12,5.9}};
approx1[t_] = Fit[testes1,{1,t,t^2},t];
approx2[t_] = Fit[testes2,{1,t,t^2,t^3},t];
tjoin = t/.FindRoot[approx1[t]==approx2[t],{t,3.0,3.1}];
V[t_]:= Which[t<=1/20,120,
              t<=7/20,V1[t],
              t<=2/5,50,
              t<=3/4,V2[t],
              t<=9/10,V3[t]];
W[t_]:= Which[t<=tjoin,approx1[t],
              t<=12,approx2[t]];
W[3]-W[1]
V[1/5]-V[1/10]
W[6]-W[3]
V[3/10]-V[1/5]
W[12]-W[6]
V[11/20]-V[3/10]