I'm trying to track a particle's velocity at each time step, but my X&Y Velocity Variables keep becoming matrices, instead of overwriting each time. How should I fix this?

The code that keeps giving me and error is

Counter = Counter + 1
TrackedVelocity(Counter) = sqrt((VelocityX)^2+(VelocityY)^2);

[Walter Roberson]

We need to see more of your code; in particular how VelocityX and VelocityY are calculated.

[cwmiller]

Here is what I have coded above what I posted...

for t = 0:DeltaT:EndTime
    
    % x,y Force and acceleration calculations 
    
    ForceY = (ParticleMass*g)+(DragForceY);      % (N)
    ForceX = (DragForceX);                       % (N)
    
    AccelY = ForceY/ParticleMass;                % (m/s^2)
    AccelX = ForceX/ParticleMass;                % (m/s^2)
    
    % Numerical Calculations that update x,y position and velocity 
    
    
    Xposition = XInitial+(XVelocityInitial*(t))+(0.5*AccelX*(t)^2);    % How would I set up an
    Yposition = YInitial+(YVelocityInitial*(t))+(0.5*AccelY*(t)^2);
    
    
    TrackedDistanceTravelled = TrackedDistanceTravelled + sqrt((Xposition)^2 + (Yposition)^2);
    % equation to find position and        
    % velocity for the first
    VelocityX = XVelocityInitial+(AccelX*(t));                              % time-step??
    VelocityY = YVelocityInitial+(AccelY*(t)); 
    
    Counter = Counter +1;
    TrackedVelocity(Counter) = sqrt((VelocityX)^2 + (VelocityY)^2);

[DGM]

I don't know what your inputs are, but for scalar inputs, this doesn't run into errors. I'm assuming some of your inputs are nonscalar and the results are becoming 2D possibly due to vector orientation and implicit array expansion, though I don't see an obvious cause.

ParticleMass = 1;
DragForceY = 1;
DragForceX = 1;
XInitial = 1;
YInitial = 1;
XVelocityInitial = 1;
YVelocityInitial = 1;
AccelX = 1;
AccelY = 1;
g = 9.81;
DeltaT = 0.01;
EndTime = 10;
TrackedDistanceTravelled = 0;
Counter = 0;

for t = 0:DeltaT:EndTime
    
    % x,y Force and acceleration calculations 
    ForceY = (ParticleMass*g)+(DragForceY);      % (N)
    ForceX = (DragForceX);                       % (N)
    AccelY = ForceY/ParticleMass;                % (m/s^2)
    AccelX = ForceX/ParticleMass;                % (m/s^2)
    
    % Numerical Calculations that update x,y position and velocity 
    Xposition = XInitial+(XVelocityInitial*(t))+(0.5*AccelX*(t)^2);    % How would I set up an
    Yposition = YInitial+(YVelocityInitial*(t))+(0.5*AccelY*(t)^2);
    TrackedDistanceTravelled = TrackedDistanceTravelled + sqrt((Xposition)^2 + (Yposition)^2);
    % equation to find position and        
    % velocity for the first
    VelocityX = XVelocityInitial+(AccelX*(t));                              % time-step??
    VelocityY = YVelocityInitial+(AccelY*(t)); 
    Counter = Counter +1;
    TrackedVelocity(Counter) = sqrt((VelocityX)^2 + (VelocityY)^2);
end

[Walter Roberson]

Suppose ParticleMass is non-scalar, then the / operator would be matrix division rather than element-by-element division, and that could lead to unexpected results.

[cwmiller]

Here is this same code in question, but with my input parameters...

%% Input Parameter Settings
clear
clc
ParticleMass = 1; % Mass of particle (kg)
 
g = -9.81;           % Gravitational acceleration (m/s^2)

DragCoefficient = 0.5;   

DeltaT = 0.001;
EndTime = 1;

XInitial = 0;               % (m)
YInitial = 0;              % (m)
 
VelocityInitial = 34;        % (m/s)
YVelocityInitial = 3;       % (m/s)
XVelocityInitial = 5;       % (m/s)
%% Model Initialization
Counter = 0;

TrackedDistanceTravelled = 0;                              %(m)

DragForceY = -DragCoefficient*(VelocityInitial)*(YVelocityInitial);         % Is this the correct way to find Drag Force in the X & Y Direction?
DragForceX = -DragCoefficient*(VelocityInitial)*(XVelocityInitial);         % ...We need it for when it just starts right?
% DragForceX/Y = DragCoefficient*(Velocity)*(X/YVelocity)
%% Time Marching 
 
for t = 0:DeltaT:EndTime
      
% x,y Force and acceleration calculations 

ForceY = (ParticleMass*g)+(DragForceY);      % (N)
ForceX = (DragForceX);                       % (N)

AccelY = ForceY/ParticleMass;                % (m/s^2)
AccelX = ForceX/ParticleMass;                % (m/s^2)
 
% Numerical Calculations that update x,y position and velocity 


Xposition = XInitial+(XVelocityInitial*(t))+(0.5*AccelX*(t)^2);    % How would I set up an
Yposition = YInitial+(YVelocityInitial*(t))+(0.5*AccelY*(t)^2);


TrackedDistanceTravelled = TrackedDistanceTravelled + sqrt((Xposition)^2 + (Yposition)^2);
                                                                            % equation to find position and        
                                                                            % velocity for the first
VelocityX = XVelocityInitial+(AccelX*(t));                              % time-step??
VelocityY = YVelocityInitial+(AccelY*(t)); 

Counter = Counter +1;
TrackedVelocity(Counter) = sqrt((VelocityX)^2 + (VelocityY)^2);

DragForceX = -(DragCoefficient*(TrackedVelocity(Counter))*(VelocityX));

if VelocityY < 0
    DragForceY = -(DragCoefficient*(TrackedVelocity)*(VelocityY));
elseif VelocityY > 0
    DragForceY = -(DragCoefficient*(TrackedVelocity)*(VelocityY));
end

if Yposition < 0
    break    
end

Answer 1

[Walter Roberson]

TrackedVelocity(Counter) = sqrt((VelocityX)^2 + (VelocityY)^2);

So TrackedVelocity is a vector that is increasing in size.

if VelocityY < 0
    DragForceY = -(DragCoefficient*(TrackedVelocity)*(VelocityY));
elseif VelocityY > 0
    DragForceY = -(DragCoefficient*(TrackedVelocity)*(VelocityY));
end

You use all of the vector TrackedVelocity in DragForceY so DragForceY is going to increase in size as you go. That is going to trigger other variables to increase in size.

Question:

Your two if branches have the same code. Therefore the difference between doing the code unconditionally and doing the code the way you do it now, is in the behaviour if neither branch of the if is met -- which would occur if VelocityY == 0 exactly or VelocityY became NaN somehow. Are you sure that in either of those cases, that you want to leave DragForceY at its previous value ?