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How to find a velocity when you have time and position values in an array?

Asked by Kelly Harmison on 21 Feb 2018
Latest activity Edited by Kelly Harmison on 21 Feb 2018
I am required to differentiate by calling values from an array. I am also required to use either a for or a while loop.

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What have you done so far? What specific problems are you having with your code? What is the relationship between velocity and position?
The main idea is to know how to differentiate on Matlab. I have two vectors: time and position. I am supposed to use a loop to call specific values from the position vector and find their slope (velocity).

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1 Answer

Answer by Roger Stafford on 21 Feb 2018
Edited by Roger Stafford on 21 Feb 2018

Let x and y be row vectors of the same length where x gives successive values of the independent variable and y the corresponding dependent variable values - in this case x values are times and y values distances. It is not necessary that x values be equally-spaced. To get a second order approximation of the derivative at each point, do this:
x1 = x([3,1:end-1]); x2 = x([2:end,end-2]);
y1 = y([3,1:end-1]); y2 = y([2:end,end-2]);
dydx = ((y2-y).*(x-x1).^2+(y-y1).*(x2-x).^2)./((x2-x).*(x-x1).*(x2-x1));
The row vector dydx will give approximate values of the derivative of y with respect to x. This is a vectorized solution - no for loops or while loops are necessary.