t = 0:0.2:25
speed1 =  (0.1553567.*t.^6 - 2.0416.*t.^5 + 9.1837.*t.^4 - 14.829.*t.^3 - 1.3703.*t.^2 + 32.821.*t - 1.3155)
speed2 = 0.003980879.*t.^5 - 0.2247.*t.^4 + 4.8682.*t.^3 - 50.442.*t.^2 + 254.67.*t - 430.66
speed3 = -0.073.*t.^2 + 6.1802.*t + 40.423

Indexing and extracting values for t < 5
idxlt5 = t < 5
tlt5 = t(idxlt5)
speedlt5 = speed1(idxlt5)

Indexing and extractiving values for 5 =< t < 15.4
idxlt154 = t < 15.4
tlt154 = t(idxlt154)
speedlt154 = speed2(idxlt154)

Indexing and exctracting values for 15.4 <= t <= 25
idxlt25 = t <= 25
tlt25 = t(idxlt25)
speedlt25 = speed3(idxlt25)

Plotting
plot(tlt5,speedlt5)
ylim([0 150])
hold on
plot(tlt154,speedlt154)
plot(tlt25,speedlt25)
hold off