How can I track and measure the velocity of a moving object in a video?

You can easily calculate the velocity multiplying the distance of centroids between previous frame and current frame, the frame rate of the video and the scale of the unit is meter/pixel.

scale = 1/320; % meter/pixel
frameRate = 30; % frame/second
velocity = velociy_pix * frameRate * scale; % pixel/frame * frame/second * meter/pixel

Here is an example code that calculates the velocity of a moving ball (requires Computer Vision System Toolbox):

%%Create a video for detection
writerObj = VideoWriter('movingBall.avi');
open(writerObj);
bgI = zeros(240,320,'uint8');
pos_org = [160 120];
r = 10;
for k = 1: 300
    f = 0.2*(1-exp(-k/200));
    pos = pos_org + 50*[cos(2*pi*f/30*k) sin(2*pi*f/30*k)];
    I = insertShape(bgI, 'FilledCircle', [pos r], 'Color', 'white');
    I = I + uint8(randn(size(I)))*10;
    writeVideo(writerObj,im2frame(I));
end
close(writerObj);

%%Calculate velocity of the ball
videoFileReader = vision.VideoFileReader('movingBall.avi');
S = info(videoFileReader);
frameRate = S.VideoFrameRate; % frame/second
scale = 1/320; % m/pixel
videoPlayer = vision.VideoPlayer('Position',[100 100 600 400]);
oldPoints = [];
while ~isDone(videoFileReader)
    videoFrame = step(videoFileReader);
    G = rgb2gray(videoFrame);
    BW = G > 0.5;
    BW2 = bwareaopen(BW, 30);
    BW3 = imfill(BW2, 'holes');
    stats = regionprops('table',BW3,'Centroid');
    points = table2array(stats);
    if ~isempty(oldPoints)
        % Calculate velocity (pixels/frame)
        vel_pix = sqrt(sum((points-oldPoints).^2,2));
        vel = vel_pix * frameRate * scale; % pixels/frame * frame/seconds * meter/pixels
    else
        vel_pix = 0;
        vel = 0;
    end

      % Visualize the velocity
      videoFrameOut = insertObjectAnnotation(videoFrame, 'circle', ...
          [points 10*ones(size(points,1),1)], ...
          cellstr(num2str(vel,'%2.2f')));
      step(videoPlayer, videoFrameOut);

      oldPoints = points;
  end
  release(videoFileReader);
  release(videoPlayer);