% sample data
t=0:0.1:10; % time
x=3+2*t+t.^2; % coordinate
[t,ind]=sort(t); % in a case time is not in an ascending order
x=x(ind);
k=find(t(1:end-1)==t(2:end)); % in a case there are coinciding times, exclude them
if ~isempty(k)
t(k)=[];
x(k)=[];
end
figure;
plot(t,x,'.-');
title('Coordinate');
xlabel('t');
ylabel('x');
% velocity
v=diff(x)./diff(t); % velocities at times tv; a vector of the length less than t, x by 1
tv = (t(1:end-1)+t(2:end))/2; % times related to v; a vector of the length less than t, x by 1
figure;
plot(tv,v,'.-');
title('Velocity');
xlabel('tv');
ylabel('v');
% acceleration
a=diff(v)./diff(tv); % accelerations at times ta; a vector of the length less than t, x by 2
ta = (tv(1:end-1)+tv(2:end))/2; % times related to a; a vector of the length less than t, x by 2
figure;
plot(ta,a,'.-');
title('Acceleration');
xlabel('ta');
ylabel('a');
