Velovity,distance and time graph sketching.

[scguy]

Differentiating a distance or displacement time graph will give the velocity at the point considered which i am sure everybody is aware, differentiating again will give the acceleration of the said object.

These facts are fine and dandy but what if i was to start with a whole bunch of data for both distance and time co-ordinates eg: (1,2.6) , (1.26, 3) , (2.57, 3.32) and so on. How do i go about turning a series of co-ordinates into an equation so that i can differentiate and find the velocity at any point? (not considering straight lines lol).

Its probably more practical to take the tangent at the point considered but i know this can be inaccurate.

[swansont]

Differentiating a distance or displacement time graph will give the velocity at the point considered which i am sure everybody is aware' date=' differentiating again will give the acceleration of the said object.

These facts are fine and dandy but what if i was to start with a whole bunch of data for both distance and time co-ordinates eg: (1,2.6) , (1.26, 3) , (2.57, 3.32) and so on. How do i go about turning a series of co-ordinates into an equation so that i can differentiate and find the velocity at any point? (not considering straight lines lol).

Its probably more practical to take the tangent at the point considered but i know this can be inaccurate.[/quote']

 

You can plot the data and fit s = vt + 1/2 at² to it. Or you can take adjacent data points and take x_n+1-x_n/t_n+1-t_n and find the average velocity - which should be the value at the midpoint of the time interval - and plot that; it assumes acceleration is a constant, and should yield a straight line.