(* the data *)
fwheeldata  :=  
        List[{0,  5.4},  {12/60,  5.71},  {16/60,  5.97},  {25/60,  
            6.80},  {40/60,  8.99}, {11 + 40/60,  
            8.74}, 
{11 + 48/60,  7.5},  {12,  
            6.17},  {12 + 18/60,  5.4},  {12 + 30/60,  
            5.71},  {12 + 47/60,  7.28}]

(* the plot of the data *)
p1  =  
        ListPlot[fwheeldata,  
          PlotStyle -> {PointSize[0.02],  RGBColor[1, 0, 0]},  
          PlotRange -> {{0,  13},  {5,  10}},  
          PlotLabel ->  "Height vs. Time",  
          AxesLabel -> {"Time (t)", "Height (m)"},  
          TextStyle -> {FontSize -> 18}]

(* the model *)

H[t_] := 
      63.4*Sin[2  Pi*(t  -  3.08)/12.3] + 
        68.8
p2 = 
      Plot[H[t],  {t,  0,  
          13},   PlotRange -> {{0,  13},  {5,  10}}]

(* the model along with the data *)

Show[p1,  p2]

R[t_] = D[H[t], t]

R[12 + 47/60]

(* Rate of change data *)
fwheelratedata  :=  
        List[{0,  -0.08},  {12/60,  3.22},  {16/60,  
            4.32},  {25/60,  6.76},  {40/60,  
            10.74}, {11 + 40/60,  -10.37}, 
{11 + 
              48/60,  -8.26},  {12,  -5.03},  {12 + 
              18/60,  -0.08},  {12 + 30/60,  3.22},  {12 + 47/60,  
            7.84}]

(* plot of the rates of change *)
p3 = ListPlot[
          fwheelratedata,  
          PlotStyle -> {PointSize[0.02],  RGBColor[1, 0, 0]},  
          PlotRange -> {{0,  13},  {-12,  12}},  
          PlotLabel ->  "Velocity vs. Time",  
          AxesLabel -> {"Time (s)", "Velocity (m/s)"},  
          TextStyle -> {FontSize -> 
                18}]

(* plot of the rates of change suitable for plotting alongside the model *)
p4  =  
        ListPlot[fwheelratedata,  
          PlotStyle -> {PointSize[0.02],  RGBColor[1, 0, 0]},  
          PlotRange -> {{0,  13},  {-33,  33}},  
          PlotLabel ->  "Velocity vs. Time",  
          AxesLabel -> {"Time (s)", "Velocity (m/s)"},  
          TextStyle -> {FontSize -> 18}]

(* the rate model along with the data-- - 
            although they will have no way of determining this model *)

Show[p4,  
      Plot[R[t],  {t,  0,  13},  
        PlotRange -> {{0, 13}, {-33, 33}}]]

Solve[
      A*Sin[2*Pi*(
MIN 
 + 
SEC
/60
)/12.3  -  
                Pi/2]  +  A  +  
          5.4 == 
HEIGHT
,  
      A]

65.8 - 59.4