Asked by Sam Thorpe
on 12 Mar 2019

Hi, I have been given a set of data which includes acceleration, velocity and time from an experiment. We have been asked to process the data in a specific manner so we can calculate the transmission loss based on some gicen equations. I am not sure how to go around starting this section. I know how to load the data but am unsure what is asking when we have to convert the acceleration into velocity. I have the following eqations given:

a=acceleration

v=velocity

t=time

v(t) =integral of acceleration with respect to time (int (a) dt) with the limits between 0 and t

and v(t)=cumsum(a)* change in t

Does anyone have any ideas on how the cumsum function changes the integration?

Thanks

Answer by Adam Danz
on 12 Mar 2019

Edited by Adam Danz
on 12 Mar 2019

Units of acceleration are typically m/s^2 (meters per second squared). Time is typically in seconds. So when you multiply (m/s^2) by (s) the results is (m/s) or, meters per second (which are the units for velocity). Multipying acceleration by the change in time gives you the change in velocity. Here's an example.

If a car is accelerating at 10 m/s^2 for 5 seconds, then 10 m/s^2 * 5 s = 50 m/s. So, there is a 50 m/s increase in velocity. But you still don't know the absolute speed of the car because you don't know it's starting speed. If the starting speed was 2 m/s then 2 + 50 = 52 m/s absolute speed.

Now let's say you have vectors of data where each element of the vector was recorded at different time points.

acceleration = [0 1 1 2 2 2 5 5 5 2 2 1 1 0]; %m/s^2

dt = 0.2; % change in time (seconds)

The instantaneous change in velocity would be

dtVel = acceleration .* dt;

And the absolute velocity would be (assumes velocity starts at 0m/s at time 0)

vel = cumsum([dtVel]); %m/s

View the data

time = dt * (0:length(acceleration)-1);

figure; plot(time, acceleration, 'b-', time, vel, 'r-')

legend('Accel.', 'Vel.')

xlabel('time (s)')

Samaneh Arzpeima
on 8 Jul 2019

thanx for the easy-to-follow explanation.I had a similular issue

can you please tell me why in

Calculate Velocity and Position

edot = (1/200)*cumsum(dataOfInterest.EastWest);

edot = edot - mean(edot);

he subtracted the mean(edot) from edot??

(1/200) is the dt in your explanation and "dataOfInterest.EastWest" the acceleration.

Thank you

Adam Danz
on 8 Jul 2019

It appears that the velocities are normalized to have a mean of 0 (or very close to zero).

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