Calculating velocity from existing data

Hello,

I am new to MATLAB and need your help.

How can i calculate the velocity when given the displacement in X and Y direction. the Data are shown in the table below:

     TIME      X        Y          
     ____    ____      
 
      0        0      0.25      
      4        4      0.25       
      9        9       0.2       
     14       14      0.15        
     24       19      0.05     
     29       24         0     
     34       29         0         
     39       34       0.1      
     44       39       0.3 

Best Regards, Youssef

[Walter Roberson]

Are we to assume smooth acceleration, or should we assume that an instantaneous impulse is applied at each of the listed times?

If we are to assume smooth acceleration, using which model?

As we are to be able to calculate velocity given displacement, and the displacements given might not be any of the ones exactly listed, are we to assume that there is some kind of potential field that is imparting acceleration, and we are to estimate what the field looks like, so that we could predict what the acceleration would be for any given X, Y pair? If so then then it would be necessary to take into account cummulative acceleration in order to figure out the acceleration at the points -- and we would not be able to tell you about velocity at given X, Y points becaused that would depend upon velocity traveling to the point.

Answer 1

[Star Strider]

Try this:

M = [       0            0         0.25
            4            4         0.25
            9            9          0.2
           14           14         0.15
           24           19         0.05
           29           24            0
           34           29            0
           39           34          0.1
           44           39          0.3];
 T1 = array2table(M, 'VariableNames',{'Time','X','Y'});
 PosXY = hypot(T1{:,2},T1{:,3});
 VelXY = gradient(PosXY)./gradient(T1{:,1});
 T2 = table(PosXY,VelXY, 'VariableNames',{'Position','Velocity'});
 T1 = [T1, T2]

producing:

T1 =

  9×5 table

    Time    X      Y      Position    Velocity
    ____    __    ____    ________    ________

      0      0    0.25       0.25     0.93945 
      4      4    0.25     4.0078     0.97247 
      9      9     0.2     9.0022      0.9993 
     14     14    0.15     14.001     0.66652 
     24     19    0.05         19     0.66661 
     29     24       0         24     0.99999 
     34     29       0         29           1 
     39     34     0.1         34      1.0001 
     44     39     0.3     39.001      1.0002 

.