t1  =   .2
t2  =   .75
v0 =  2/(t2 - t1 + 1.0)

d1[t_] := v0*t*t/(2*t1)
d2[t_] := v0*t1/2 + v0*(t - t1)
d3[t_] := 
      v0*t1/2 + 
        v0*(t2 - 
              t1) + (v0 - (v0*(t - t2)/(1 - t2))/2)*(t - 
              t2)

p1 = Plot[d1[t], {t, 0, t1}]

p2 = 
      Graphics[{PointSize[0.025], 
          Point[{t1, v0*t1*t1/(2*t1)}]}]

p3 = Plot[d2[t], {t, t1, t2}]

p4 = 
      Graphics[{PointSize[0.025], 
          Point[{t2, v0*t1/2 + v0*(t2 - t1)}]}]

p5 = Plot[d3[t], {t, t2, 1.0}]

Show[p1, p2, p3, p4, p5]