How to Use Numerical Integration

How do you do numerical integration for the velocity when given the time and acceleration? I also know that this data is first recorded when the rocket has a velocity, vi, of -250 m/s and that the integral of acceleration is velocity. Using numerical integration, I need to calculate the velocity as a function of time. the data is taken every .001 seconds. below is what I have coded so far and attached is the data excel sheet.

%% Data

data = xlsread('Rocket.xls');

t = data(:,1);

a = data(:,2);

%% Rockets Velocity??

Answer 1

[Star Strider]

If your data are vectors, use the cumtrapz or trapz function, depending on what result you want.

For example:

v = cumtrapz(t, a);                                 % Calculate Velocity
d = cumtrapz(t, v);                                 % Calculate Displacement

[Victoria Lucero]

I got this error:

Error using cumtrapz (line 71) LENGTH(X) must equal the length of Y in dim 1.

Error in P4 (line 27) v = cumtrapz(t, a);

[Star Strider]

I don’t have your data, so I assumed they were the same lengths.

You would first have to shorten the longer vector, and since I don’t know which one that is, I have to generalise.

Do this first:

L = min(length(t),length(a));
a = a(1:L);
t = t(1:L);

then do the integrations.