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Help with approximation first/second derivative velocity/accel

I have a table of values for a projectile moving away from a radar station. My first column is the time (t) of 0 to 60 with time steps of 4. I then have a distance(km) of the projectile from the radar station followed by the angle(radians) of the projectile to the radar station.

The distance obviously increases by time along with a lowering of the angle of the projectile to the radar station.

I need to write a program which will work out the magnitude of velocity and acceleration for each time step (each 4 seconds upto 60) as the projectile moves away. I am confused how to do this because I am unsure how to approximate the derivatives. I can give further data and formulas if required. The program is the easy bit but I just don't know how to get the write answers into Excel first so I can work out how to program it correctly.

I think that what you are having is a dilemma between thinking in a cartesian system and having data in a polar system. Thus what you need is to look at the derivatives of a polar system of coordinates in relation to the derivatives of the cartesian system that you want. I am happy to explain this to you - but I think it is something that would be easier to do were you present at the time, thus if you would like more information please contact me. :-D
11 December 2014
The coordinate system doesn't really matter provided that you are consistent.  You could convert your data into a cartesian system using x=RCos(a)  y=RSin(a).  You then have a set of x,y coordinates.  The distance between adjacent data points can be obtained courtesy of Pythagoras.  The velocity is that distance divided by the time interval.  The acceleration is the difference between adjacent values of velocity.
15 December 2014
Hello, this is not that difficult to accomplish on Excel or MATLAB. I could code it up for you if you would be kind enough to give me the table that you talk about.
03 January 2015
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