k1 =  .2
k2 = 0.75

k11  =  k1*2/Pi

p1 = Plot[k11*(Sin[u/k11 - Pi/2] + 1), {u, 0, k1}]

p2 = Graphics[Line[{{k1, k11}, {k2, k11 + (k2 - k1)}}]]

p3  =  Graphics[{PointSize[0.025], Point[{k1, k11}]}]

p4  =  
      Graphics[{PointSize[0.025], 
          Point[{k2, k11 + (k2 - k1)}]}]

p5 = 
      Plot[((1 - k2)/(Pi/
                    2))*(Sin[(u - 
                      k2)*(Pi/2)/(1.0 - k2)]) + 
          k11 + (k2 - k1), {u, k2, 1.0}]

Show[p1, p2, p3, p4, p5, PlotRange -> {{0.0, 1.0}, {0.0, 1.0}}, 
      AspectRatio -> 1, 
      AxesLabel -> {"time", "distance"}]

s  =  k1*2/Pi  +  k2 - k1  +  (1.0 - k2)*2/Pi

q1 = 
        Plot[(k11*(Sin[u/k11 - Pi/2] + 1))/s, {u, 0, 
            k1}];

q2 = 
      Graphics[Line[{{k1, 
              k11/s}, {k2, (k11 + (k2 - k1))/s}}]]

q3  =  Graphics[{PointSize[0.025], Point[{k1, k11/s}]}]

q4  =  
      Graphics[{PointSize[0.025], 
          Point[{k2, (k11 + (k2 - k1))/s}]}]

q5 = 
      Plot[(((1 - k2)/(Pi/
                        2))*(Sin[(u - 
                          k2)*(Pi/2)/(1.0 - k2)]) + 
              k11 + (k2 - k1))/s, {u, k2, 1.0}]

Show[q1, q2, q3, q4, q5, PlotRange -> {{0.0, 1.0}, {0.0, 1.0}}, 
      AspectRatio -> 1, 
      AxesLabel -> {"time", "distance"}]