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How do I calculate acceleration with velocity and the code given?

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Michelle Wilcock
Michelle Wilcock on 25 Jan 2020
Edited: Vladimir Sovkov on 25 Jan 2020
So this is how I got the velocity done and graphed but I can't figure out how to get the acceleration done. I get an error that the matrix dimensions aren't the same. I'm stuck as to where to go from here and can't find information regarding the code I need to use.
v=zeros(1,length(t)); % Create the velocity array - initially filled with zeros
v(1)=(x(2)-x(1))/(t(2)-t(1)); % first velocity point - method 1
v(2:end-1)=(x(3:end)-x(1:end-2))./(t(3:end)-t(1:end-2)); % method 3
v(end)=(x(end)-x(end-1))./(t(end)-t(end-1)); % last point - method 2
Calculation of acceleration versus time using numerical derivatives
a=zeros(1,length(t)); % Create the acceleration array
a(1)=diff(v(1))./diff(t);
a(2:end-1)=a1(end);
a(end)=gradient(v,0.01);

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Answers (1)

Vladimir Sovkov
Vladimir Sovkov on 25 Jan 2020
Edited: Vladimir Sovkov on 25 Jan 2020
% 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');

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